What are the next entries for the following sequences?

  • A : 1, 11, 21, 1211, 111221, ? ...
  • B : 1, 11, 101, 111011, 11110101, ? ...
  • C : 4, 484, 28224, 228484, 8282884, ? ...
  • D : 1, 1, 2, 3, 5, 8, 13, 21, ? ...
  • E : 1, 1, 2, 5, 14, 42, ? ...
  • F : 1, 1, 2, 5, 15, 52, ? ...
  • G : 1, 3, 13, 63, 321, 1683, ? ...
  • H : 1, -1, 1, -3, 17, -155, 2073, ? ...
  • I : 1, 1, 3, 7, 19, 51, 141, ? ...
  • J : 1, 2, 5, 13, 35, 96, ? ...
  • K : 2,3,6,7,8,11,12,15,18,19,22,23,24,27,28,31,32,33,43,44,47,48,?...
  • L : 1, 2, 3, 5, 7, 11, 15, 22, 30, ?...
  • M : 1,1,2,3,3,4,5,5,6,6,6,8,8,8,10,9,10,11,11,12,12,12,12, 16,14,14,16,16,16,16,20,?...
  • N : 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, ? ...
  • O : 1, 20, 400, 8902, 197742, 4897256, 120921506, ? ...
  • P : 1, 2, 12, 576, 161280, 812851200, ? ...
  • Q : 1, 1, 2, 5, 12, 35, 108, ? ...
  • R : 1, 2, 2, 3, 4, 7, 14, 42, ? ...
  • S : 1, 2, 3, 4, 6, 8, 10, 13, 17, 21, 27, 30, 37, 47, 57, 62, 75, 87, ?...
  • T : 1, 1, 2, 3, 6, 10, 20, 37, 74, 142, ?...
  • U : 2642242888682886824484644846... ?
  • V : 1, 2, 3, 5, 6, 8, 10, 11, 12, 14, 16, 18, 20, ?...

    • References:

  • Martin Gardner; Mathematical Games: Patterns in Primes are a Clue to the Strong Law of Small Numbers, Scientific American 243, December 1980, 18-28
  • Richard K. Guy; The Strong Law of Small Numbers, AMM 95:8 (Oct. 1988) 697-712
  • Richard K. Guy; The Second Strong Law of Small Numbers, Math. Mag. 63:1 (Feb. 1990) 3-20
  • N. J. A. Sloane & S. Plouffe; The Encyclopedia of Integer Sequences, Academic Press, (1995) ISBN 0-12-558630-2, $44.95, 587pp., 5487 sequences. There is also a floppy disk with the sequences on it (not the descriptions) for $10.00.
  • N. J. A. Sloane; Integer Sequences web page; http://www.research.att.com/~njas/sequences/
  • J. H. Conway; Testing for linear recurrence relations, e-mail to math-fun, (Oct. 1994)
  • Carl E. Linderholm; Linderholm's universal rule, Wolfe Publishing, 1971
  • Torsten Sillke; Autocorrelation sequences of binary (and trinary) strings
  • Torsten Sillke; Autocorrelation Range and the table 1-1025
  • Torsten Sillke; Factors of the Morse Thue Sequence
  • Bjorn Poonen, Michael Rubinstein; The number of intersection points made by the diagonals of a regular polygon - a ps-file
  • Neil J. A. Sloane; electronic Journal of Integer Sequences
  • Richard P. Stanley; Problems on Catalan and Related Numbers, excerpted from 'Enumerative Combinatorics' vol. 2.
  • tiling the n-square with 1x1 and 1x2 tiles - 1 7 131

    • To lookup sequences in the On-Line Encyclopedia of Integer Sequences, send mail to sequences@research.att.com containing lines of the form lookup 4 9 16 25 36 lookup 3 5 8 13 21 If there are no such lines, you will get a file explaining the notation.
    My favorite quotation from a reader of the 1973 book:

    Neil Sloane
    Sequentially yours, The On-Line Encyclopedia of Integer Sequences

    Torsten Sillke , 24.08.98