Integer Sequence

A Sequence whose terms are Integers. The most complete printed references for such sequences are Sloane (1973) and its update, Sloane and Plouffe (1995). Sloane also maintains the sequences from both works together with many additional sequences in an on-line listing. In this listing, sequences are identified by a unique 6-Digit A-number. Sequences appearing in Sloane and Plouffe (1995) are ordered lexicographically and identified with a 4-Digit M-number, and those appearing in Sloane (1973) are identified with a 4-Digit N-number.

Sloane's huge (and enjoyable) database is accessible by either e-mail or web browser. To look up sequences by e-mail, send a message to either mailto:sequences@research.att.com or mailto:superseeker@research.att.com containing lines of the form lookup 5 14 42 132 .... To use the browser version, point to http://www.research.att.com/~njas/sequences/eisonline.html.

See also Aronson's Sequence, Combinatorics, Consecutive Number Sequences, Conway Sequence, Eban Number, Hofstadter-Conway $10,000 Sequence, Hofstadter's Q-Sequence, Levine-O'Sullivan Sequence, Look and Say Sequence, Mallow's Sequence, Mian-Chowla Sequence, Morse-Thue Sequence, Newman-Conway Sequence, Number, Padovan Sequence, Perrin Sequence, RATS Sequence, Sequence, Smarandache Sequences

References

Aho, A. V. and Sloane, N. J. A. ``Some Doubly Exponential Sequences.'' Fib. Quart. 11, 429-437, 1973.

Bernstein, M. and Sloane, N. J. A. ``Some Canonical Sequences of Integers.'' Linear Algebra and Its Applications 226-228, 57-72, 1995.

Erdös, P.; Sárközy, E.; and Szemerédi, E. ``On Divisibility Properties of Sequences of Integers.'' In Number Theory, Colloq. Math. Soc. János Bolyai, Vol. 2. Amsterdam, Netherlands: North-Holland, pp. 35-49, 1970.

Guy, R. K. ``Sequences of Integers.'' Ch. E in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 199-239, 1994.

Krattenthaler, C. ``RATE: A Mathematica Guessing Machine.'' http://radon.mat.univie.ac.at/People/kratt/rate/rate.html.

Ostman, H. Additive Zahlentheorie I, II. Heidelberg, Germany: Springer-Verlag, 1956.

Pomerance, C. and Sárközy, A. ``Combinatorial Number Theory.'' In Handbook of Combinatorics (Ed. R. Graham, M. Grötschel, and L. Lovász). Amsterdam, Netherlands: North-Holland, 1994.

Ruskey, F. ``The (Combinatorial) Object Server.'' http://sue.csc.uvic.ca/~cos/.

Sloane, N. J. A. A Handbook of Integer Sequences. Boston, MA: Academic Press, 1973.

Sloane, N. J. A. ``Find the Next Term.'' J. Recr. Math. 7, 146, 1974.

Sloane, N. J. A. ``An On-Line Version of the Encyclopedia of Integer Sequences.'' Elec. J. Combin. 1, F1 1-5, 1994. http://www.combinatorics.org/Volume_1/volume1.html#F1.

Sloane, N. J. A. ``Some Important Integer Sequences.'' In CRC Standard Mathematical Tables and Formulae (Ed. D. Zwillinger). Boca Raton, FL: CRC Press, 1995.

Sloane, N. J. A. ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.

Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego, CA: Academic Press, 1995.

Stöhr, A. ``Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe I, II.'' J. reine angew. Math. 194, 40-65 and 111-140, 1955.

Turán, P. (Ed.). Number Theory and Analysis: A Collection of Papers in Honor of Edmund Landau (1877-1938). New York: Plenum Press, 1969.

Weisstein, E. W. ``Integer Sequences.'' Mathematica notebook IntegerSequences.m.