A368358 Consider the doubly-infinite permutation P defined on page 87 of Davis et al. (1977); sequence gives the terms starting at and to the left of 1, in reverse order.

1, 4, 6, 5, 7, 16, 24, 20, 28, 18, 26, 22, 30, 17, 25, 21, 29, 19, 27, 23, 31, 64, 96, 80, 112, 72, 104, 88, 120, 68, 100, 84, 116, 76, 108, 92, 124, 66, 98, 82, 114, 74, 106, 90, 122, 70, 102, 86, 118, 78, 110, 94, 126, 65, 97, 81, 113, 73, 105, 89, 121, 69, 101, 85, 117, 77, 109

Offset

0,2

Comments

P is a doubly-infinite sequence which is a permutation of the positive integers and contains no increasing or decreasing 4-term arithmetic progression.

A central portion of P, showing terms to the left (the present sequence) and right (A368357) of the central 1:

..., 18, 28, 20, 24, 16, 7, 5, 6, 4, 1, 2, 3, 8, 12, 10, 14, 9, 13, 11, 15, ...

See the link for a larger portion.

Links

Table of n, a(n) for n=0..66.

Davis, J. A.; Entringer, R. C.; Graham, R. L.; and Simmons, G. J.; On permutations containing no long arithmetic progressions, Acta Arith. 34 (1977), no. 1, 81-90. The recurrence defining P is given in Fact 6 on page 87.

N. J. A. Sloane, A portion of P showing 511 consecutive terms around 1

N. J. A. Sloane, Maple code

Crossrefs

Cf. A003407, A368357 (the right-hand portion).

Sequence in context: A199289 A306341 A306654 * A114602 A110000 A073922

Adjacent sequences: A368355 A368356 A368357 * A368359 A368360 A368361

Keyword

nonn

Author

N. J. A. Sloane, Dec 31 2023

Status

approved