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

Author

Benoit Cloitre, Jun 03 2002

Keywords

• nonn

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

Crossrefs

Cf. A005839.

Extensions

More terms from Rémy Sigrist, Mar 14 2023