A071711 Let s(k) denote the k-th term of an integer sequence such that s(0)=0 and s(i) for all i>0 is the least natural number such that no four elements of {s(0),..,s(i)} are in arithmetic progression. Then it appears that there are many set of 3 consecutive integers in s(k). Sequence gives the smallest element in those triples.

0, 7, 14, 28, 48, 55, 64, 86, 108, 168, 286, 371, 471, 633, 760, 982, 1032, 1136, 1261, 1600, 1739, 1788, 1822, 1848, 3832, 4225, 5504, 7729, 8062, 9229, 10110, 21977, 27953, 39335, 50820, 50852, 86357, 95586, 106331, 160418, 295806, 314853, 368358, 459825

Offset

1,2

Comments

Presumably there are infinitely many such triples.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..90

K. S. Brown, Sequences With No Arithmetic Progressions

Rémy Sigrist, C++ program

Prog

(C++) See Links section.

Crossrefs

Cf. A005839.

Sequence in context: A158204 A115815 A275241 * A290398 A033895 A196876

Adjacent sequences: A071708 A071709 A071710 * A071712 A071713 A071714

Keyword

nonn

Author

Benoit Cloitre, Jun 03 2002

Extensions

More terms from Rémy Sigrist, Mar 14 2023

Status

approved