Fortean Mysteries SIG    recent history            issue 81      
      
Newsletter of the Fortean Mysteries SIG of American Mensa          
  only 200,000 millicents per 3 issues                                Published irregularly since Undecember 1658 AC
 "All things are possible ..." (Mt 19:26)

 SEQUENCES (RE)DISCOVERED
   We recently discovered  website of the On-line Encyclopedia of Integer Sequences by N. J. A. Sloan, www.research.att.com/~njas/sequences, and discovered several of our favorite ones were not included in its 70,000+ entries. We submitted some and got them accepted. Rather mysterious-looking, aren't they? (Exercise your brain and see if you can spot the patterns before reading the generating rule.)

I. 0 1 7 2 5 8 8 3 11 5 9 9 8 9 9 4 9 12 14 7 7 11 12 10
II. 10 11 13 41 51 16 17 81 91 30 13 33 43 53 63 73
III. 1000 1000000000 1000000000000000000000000000 100 1 4 8 3 5
IV. 5 6 8 9 11 12 13 15 16 18 19 25 26 28 29
V. 1 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 30 31 33 34 35 36 37 38 39 40 41 43 44
VI. 1652100 31946 38760 49537526 732051 724298 36969 47723135 24375809
VII. 18 666 23994 679 31 1134 40842 1470330 681 33 1206 43434 1563642 43974
VIII. 1 2 3 4 7 10 14 17 20 21 22 23 24 27 40 41 42 43
IX. 0 3 6 8 9 30 33 36 38 39 60 63 68 69 80 83 86 89 90 93 96 98 99 300 303
X. 2 5 22 25 52 55 222 225 252 255 522 525 552 555 2222 2225 2252 2255
XI. 11 101 11 101 11 101 11 101 11 22 112 22 112 22 112 22 112 22 112 202 112 202 112
XII. 5 2 5 2 5 2 5 2 5 2 4 2 4 2 4 2 4 2 4 3 2 3 2 3 2 3 2 3 2 3 4 2 4 2 4 2 4 2 4 3 2
XIII. 10000 10001 10002 10003 10004 10005 10006 10007 10008 10009 10010
XIV. 3 141 5926535 89793238 4626433 8327950 2 88 4 1971 6939975 10 5 820
XV. 11 22 33 44 55 66 77 88 99 110 111 112 113 114 115 116 117 118 119 220 221 222
XVI. 0 1 2 4 6 8 9 10 11 12 14 16 18 19 20 21 22 23 24 26 28 29 40 41 42 44 46 48
XVII. 3 14 15 92 6535 8979 323846 26433832 795028 841971 69399375
XVIII. 5 3 6 2 3 7 2 3 5 4 2 4 8 3 2 3 6 3 2 3
XIX. 1 3 6 7 8 9 10 13 16 17 18 19 30 31 33 36 37 38 39 61 63 66 67 68 69 70 71 73
XX. 4 2 3 6 2 3 7 2 3 5 4 2 4 8 3 2 3 6 5 2 3 5
XXI.  3 5 6 7 9 10 11 12 13 15 16 17 19 20 23 25 26 27 29 30 33 35 36 37 39 50 53
XXII. 1 2 4 8 14 18 21 22 24 28 31 32 34 38 40 41 42 43 44 45 46 47 48 49 51 52
XXIII. 101,000 1010,000 10100,000 101,000,000 1010,000,000 10100,000,000 101,000,000,000 1010,000,000,000
XXIV. 1728 20736 248832 2985984 35831808 429981696 5159780352
XXV. 0 1 4 8 9 10 16 25 36 40 49 64 80 81 100 121 125 144 160 169 196 216 225 250
XXVI. 1 2 5 6 7 8 9 10 11 12 15 16 17 18 19 20 29 50 51 52 55 56 57 58 59 60 61 62 65 66 67 68 69 70 71 72 75 76 77 78 79 80 81 82 85 86 87 88 89 90 91 92 95 96 97 98 99 1000000000
XXVII. 0 1 2 4 5 6 8 10 24 26 40 46 64 84 200 206 600 5000  
XXVIII. 120 121 123 124 125 126 127 128 129 320 321 323 324 325 326 327 328
XXIX. 1, 16, 1.26630716... x 103,638,334,640,024
XXX. 0 2 3 4 8 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
XXXI. 1 18 24 2753 59 62 95 98 126 132 135
XXXII. 3 141 592 653 58979 3238462 6433832 7950288 419716939 9375105820
XXXIII. 12 21 22 2324 25 26 27 28 29 32 42 52 62 72 82 92 102 112 122 132 142
XXXIV 142857 5882352941176470 526315789473684210 4347826086956521739130 3448275862068965517241379310
2127659574468085106382978723404255319148936170
XXXV. 1 5 10 25 40 63 84 110 135 159 192 230 265 294 330 366 397 434 455 483
XXXVI. 5 3 6 2 3 7 2 3 5 4 2 4 8 3 2 3 6 3 2 3 5 3 2 3 6 5 2 3 5 5 2 3 5 3 2 3 7 5 2 3 6 4 2 3 5 4 2 3 5 2 2 3 8 4 23 7 5 2 3 5 2 3 2 3 9 5 2
XXXVII. 4 2 3 6 2 3 7 2 3 5 4 24 8 3 2 3 6 5 2 3 5 3 2 3 6 3 2 3 5 5 2 3 5 5 2 3 7 3 2 3 6 5 2 3 5 4 2 3 5 4 2 3 8 3 2 3 7 5 2 3 5 2 3 2 3
XXXVIII.  11 12 15 24 36 111 112 115 128 132 135 144 175 212 216 224 312 315 384 432 612 624 666 672 735 816 1111 1112 1113 1115 1116  
XXXIX. 1 265,536
XXXX. 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24  25 26 27 28 29 30 32 33 34 35 37 38 39 40
XXXXI. 11318 15216 10799546 129618 125258 14118 10211981 2839691 282506
XXXXII. 9 252 6813 265 22 603 16290 439839 267 24 657 17748 479205 17761 670 18099 488682 13194423 17763 672 18153 490140 13233789 490153 18166 490491
XXXXIII. 1 9 31 36 98 107 156 164 210 221 266 312 358 365 405 415 460 467 509 519 548 556 564 566 571 577 587
XXXXIV. 3 14 15 96 535 897 933 8466 43383 79502 88419 716939 937510
XXXXV. 3 14 19 23 89 793 2384 2433 8327 9028 84197 193993 710820 974944
XXXXVI.  3 11 59  535 8979 33833 83795  88197 193993 751589 795937 818899
XXXXVII. 3 14 19 26 89 92 846 2648 2902 8841 9169 9910 82094 944920 816406  
XXXXVIII. 4 26 82 84 626 4820 28846 10820 44420 86406 286208 862804
XXXXIX. 3 11 59 535 897 933 8338 37950 197169 399375 1058097 9593071
L. 2 10 30 68 130 222 350 520 738 2 4 12 32 70 132 224 352 522 740 10 12 20 40
LI. 1 2 5 8 9 10 11 12 15 18 19 20 21 22 25 28 29
LII. 1 2 2.799137013...x10507(1010)142,581
LIII. 0 1 4 7 64 100 101 104 107 343 401 404 407 700 701 704 707 764
LIV. 1 4 11 16 19 29 33 42 56 70 71 74 77 87 105 109 121 128 132 142 151 161 166
LV. 3 6 27 12 15 216 21 24 729 30 33 9 39 42 126 48 51 513 57 60 9 66 69 72 75 78
LVI. 4 4 3 5 4 3 5 4 3 4 5 4 4 4 3
LVII. 1 5 6 7 9 11 1000000 1000001 1000005 1000006 1000007 1000009 1000011
LVIII. 2 9 16 23 30 6 -142 -600 -1678 -3841 -7740 -14243 -24466
LIX. 1 2 5 6 7 8 9 10 11 12 15 16 17 18 19 20 21 22 25 26 27 28 29 50 51 55 56 57 58
LX. 2 40 42 50 52 90 92 200 240 242 250 252 290 292 2000000 2000002
LXI. 0 8 69 96 609 689 906 986 6009 6699 6889 6969 9006 9696 9886 9966
LXII. 5 6 7 9 11 500 505 506 507 509 511 600 605 606 607 609 611 700 705 706

I. The most interesting one is perhaps that involved with the 65-year-old unsolved 3n+1 problem. All integers seem to be reducible to 1, but it hasn't been proven yet. modified Collatz: [Collatz or hailstone delay sequence, A008577, modified to allow application of  3x+1 operation on even numbers for reduced delay, D(n)] The sequence, is generated by applying the HOTPO operator on the integers until each is reduced to 1and listing the number of steps needed. The number of steps for 9, for example, is 119 in the unmodified Collatz. It's also called a hailstone sequence because the HOTPO operator makes the integer go up and down apparently at random like a hailstone in a hailstorm.
II. abntu: [pronounced “ab-`n-too”, “Word Weirdness”, Mpossibilities 66:5, Feb. 1998, Bantu alphabeticalized, A072809]  
III. alphabetical numeration: [“Alphabetical Numeration”, Puzzle-M (Feb. 1987), least number containing each letter of alphabet, using base 36 values for jillion and kazillion, related to A053433]
IV. Ariel: [antonym of Caliban, with a, c, i or l] complement to Caliban
V. Bantu: [“Word Weirdness”, Mpossibilities 66:5, (Feb. 1998), from “ban two”]
VI. base-36: [number names converted from base 36 in which 10 = A, 11 = B, ..., Z = 35, A072922]
VII. base-36 Roman numerals: [Roman numerals converted from base 36]
VIII. Caliban: [without a, c, i, l, A072958]
IX. curvaceous: [“Three Boxes”, Puzzle-M (Apr. 1987), with digits having curved lines, A072960]
X. curvilinear: [“Three Boxes”, Puzzle-M (Apr. 1987), with digits having both curved and linear lines, A072961]
XI. DENEAT: [“Blackholing”, Mpossibilities 69:2, (Jan. 1999), “digits -- even, not even and total”, Michael Ecker, New Scientist Dec. 1992, A073053]
XII. deneaticity: [“Blackholing”, Mpossibilities 69:2, (Jan. 1999), Michael Ecker, “Caution: Black Holes at Work”, New Scientist Dec. 1992, “digits -- even, not even and total”, A 073054]
XIII. diamond: [Robert E. Smith, number with n2+(n-1)2 digits arrangable in diamond, 104 to 105-1, then 1012 to 1013-1, etc.]
XIV. diced pi: [pi divided into integers in (and alternately outside) cube digits, 0, 1 or 8, with initial 0 understood when number ends in cube]
XV. double-header: [number with first two digits identical]
XVI. ellav: [“Word Weirdness”, Mpossibilities 66:6 (Feb. 1998), ananym of valle, without 3, 5, 7]
XVII. evenly sliced pi : [pi sliced into ever increasing even-digited integers]
XVIII. five's: [“Newies”, Mpossibilities 64:3 (Mar. 1997), A072424, from the generating sentence: "Five's the number of letters in the first word of this sentence, three in the second, six in the third, two in the fourth, three in the fifth ..."]
XIX. flawless: [without a, f, l, w]
XX. four-ises: [“Newies”, Mpossibilities 64:3 (Mar. 1997) On-line Encyclopedia of Integer Sequences by N. J. A. Sloan, A072425, f rom the generating sentence: "Four is the number of letters in the first word of this sentence, two in the second, three in the third, six..."]
XXI. godless: [finite sequence without d, g, o]
XXII. godly: [with d, g, o]
XXIII. great googol: [Mpossibilities 74:6 Aug. 2000, from analogy, gross:great gross::googol:?]
XXIV. great gross [12n+2]
XXV. Haken: [decimal multiples or squares or cubes
XXVI. harmless: [without a, h, m, r]
XXVII. heterogram: [Susan Thorp, with no letters repeated, A059916]
XXVIII. intwo: [number with 2 in interior, but on neither end]
XXIX. JGE: [Joyce Generalized Exponential, G(n1, n2, n3, ..., nm-2, nm-1, nm) = G( n1, G(n1-1, n2, n3, ..., nm-2, nm-1, nm), nm), G(m, n, p, q) = Gm(n, p, q) = Gm-1(n, G(n, p, q), p), G(n, ..., n)]
XXX. nabrut: [ ananym of turban]
XXXI.  n-ests: [“Newies”, Mpossibilities 64:3 (Mar. 1997) On-line Encyclopedia of Integer Sequences by N. J. A. Sloan, A072422 (July 31, 2002), from the generating sentence, “N est prima littera in hic sententiam, doudevicesima littera in hic sententiam, quarta vicesima littera in hic sententiam, septima vicesima littera in hic sententiam, tertia quinquagentesima littera in hic sententiam ...."] XXXII. oddly sliced pi: [pi sliced into ever increasing odd-digited integers]  
XXXIII. ontwo: [“Word Weirdness”, Mpossibilities 66:5 (Feb. 1998), with 2 on either end
XXXIV. persistent: [“Overbyte”, Mpossibilities 62:2 (Apr. 1996), Believe It or Not by Robert Ripley (1929), number whose sequence of digits persists when multiplied, [10p-1/p], at least in the first few cases the rounded quotient of ten-to-a-prime-minus-one over the so-called repetend prime, A006883]
XXXV. p-ests: [“Newies”, Mpossibilities 64:3 (Mar. 1997), On-line Encyclopedia of Integer Sequences by N. J. A. Sloan, A072421 (July 31, 2002), from the generating sentence, "P est prima praeterea quinta praeterea decima praeterea quinta vicesima praeterea quadragesima praeterea tertia sexagesima praeterea quarta octogesima praeterea decima centesima ... littera in hic sententiam."]
XXXVI. pfive's: [five's that is also palindromic]
XXXVII. pfour-is: [four-is that is also palindromic]
XXXVIII. podd: [number whose product-of-digits divides the number, notable in that a(666) = 666]
XXXIX. RGE tactorial: [“New Ways to Get High”, Mpossibilities 70:4 Mar. 1999, Recursive Generalized Exponential, !n!G(!n!, !n!, !n!)]
XXXX. s-ain't: [“When the S-ain'ts ...”, Mpossibilities 61:1-2 (Feb 1996), A072886, numbers generated like the Aronson series from a generating sentence, "S-ain't the second, third, fourth, fifth . . . letter of this sentence.".]
XXXXI. Sallows': [integers in Lee Sallows' base-27 system where space = 0, A = 1, B = 2, etc., A072959]
XXXXII. Sallows' Roman numerals: [Roman numerals evaluated as if in Sallows' base 27]
XXXXIII. s-inner: [“When the S-ain'ts ...”, Mpossibilities 61:1-2 (Feb 1996), A072887, numbers generated like the Aronson series from a generating sentence, "S-ain't the second, third, fourth, fifth . . . letter of this sentence.”]
XXXXIV. sliced Bantu pi: [pi without 2, sliced into ever increasing integers]
XXXXV. sliced Caliban pi: [pi without 5, 6 sliced into ever increasing intergers] XXXXVI. sliced eban pi: [pi without digits with e, (0, 2, 4, 6), sliced to form ever increasing integers,
XXXXVII. sliced ellav pi: [Mpossibilities 66:6, ananym of valle, term from Paguingue, without 3, 5, 7, sliced into ever increasing integers]
XXXXVIII. sliced even pi: [Mpossibilities 64:3, pi without odd digits; sliced into ever incresing integers]
XXXXIX. sliced evenly-evenly pi: [Mpossibilities 64:2, 80, pi without 2, 4 or 8 digits; sliced to form ever increasing integers]
L. SODAC: [ “sum of digits and cubes]
LI. suburban: [without b, r, s, u, A072955]
LII. tactorial: [“New Ways to Get High”, Mpossibilities 70:3, Mar. 1999, !n! = !(n!)]
LIII. Taliban: [without letters a, i, l, t, A072954]
LVI. t-ests: [A072423, from the generating sentence: "T est prima et quarta et undecima et sexima decima et nona decima et nona vicesima ... littera in hic sententiam."]
LV. TOSCOD: [“triple or sum cubes of digits”]
LVI. toscodicity: [A72420, number of operations of TOSCOD to tranform n to 153]
LVII. turban: [without letters r, t, u, A072956]
LVIII. unexpected: [Mpossibilities 36:4, a(n) = 7n - 5 - 31(n-1)(n-2)(n-3)(n-4)(n-5)/5!, alternative answer to “2 9 16 23 30 6 ?”, said to be best answered with 7n + 2 (mod  31) from calendar]
LIX.  urban: [without r, u, A072957]
LXXIII. useless: [without e, s, u]
LXXIV. vertical palindromes: [numbers that read the same up-side-down]
LXXV. worthless: [without h, o, r, t, w]

PARANORMAL INSIDER {Aug. 17, 2002)
Concluded Dr. Wise, "It would be easy to conclude that these elderly people had entered the early stages of senile dementia. However, not all experts agree that brain functions degenerate to this degree as we age. An alternate explanation by some in the paranormal community is that frail old people are more vulnerable to attack by unseen entities that gain mischievous pleasure from altering their beliefs and behavior.”
Live On TV: The Loch Ness Monster! You might just catch a live glimpse of Nessie when you visit the camvista.com web site. That's because the company has a camera mounted on Deepscan, the research vessel of the Loch Ness Project. Headed by Adrian Shine, the project offers live pictures from the ship's deck as well as from the vantage point of an underwater camera that is periodically lowered into the depths.

NEWS OF THE WEIRD
Mary Palmieri, Enfield, Conn., is now homeless after she allowed pagan “friends” to perform a ritual in her house to "burn her troubles away." The witchcraft ritual involved burning a piece of paper with Mary's problems written on it. The flames got out of control and set fire to the house. Mary's bedroom was gutted and the house suffered extensive smoke and water damage. Mary says next time she will talk to her priest instead.

"A woman, who told Roswell Police she had been on another planet for three years, reported a robbery Friday. She said a known person had taken the upper plate of her dentures valued at $800, silverware in a wooden box valued at $1,000, and various jewelry worth $1,000. She said she hadn't actually seen the named suspect take the items, but he 'moves so swift you can't see him.'" [Roswell Daily Record, 5-29-01]
In preparation for the founding meeting of a new political group (the Anambra Peoples' Forum) in Lagos, Nigeria, in March, officials concerned about being rained out hired a professional rain doctor, Mr. Chief Nothing Pass God, for about $47 (and a bottle of gin) to keep the skies clear. Before the doctor was finished with his incantations, a rare March downpour completely washed out the event. Said the Chief, "I have not failed. What caused the disappointment was that (this job) came unexpected(ly)" and that he had not had sufficient time to prepare. [South African Press Association-Agence France-Presse, 3-18-02]

 BIZARRE NEWS
When Kathleen Healy, Rosedale, Minn., entered the Marshall Field's dressing room, she found a money clip full of cash. Though she could see a $50 and $100 bill, she didn't count it all because "it wasn't my money," she said. She then gave the wad to the clerk and refused any reward. The sales clerk "screamed and said 'Oh, a customer's been looking all over for this.'" The frantic customer burst into tears of relief when they returned the cash to her, but Healy still refused a reward. The sales clerk insisted she take a box of Marshall Field's signature chocolates, Frango Mints. When Healy opened the box, a note was enclosed indicating she had won $10,000. As part of their "Win a Mint" game. "I've never won anything before. I've never won a toaster," the ecstatic winner said.

COMING NEXT ISSUE ---
           THE TRUTH (MORE OR LESS) ABOUT CROP CIRCLES
[For more strange sequences see Sequences.]