A071711 - OEIS

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.

%I #14 Mar 14 2023 17:24:43

%S 0,7,14,28,48,55,64,86,108,168,286,371,471,633,760,982,1032,1136,1261,

%T 1600,1739,1788,1822,1848,3832,4225,5504,7729,8062,9229,10110,21977,

%U 27953,39335,50820,50852,86357,95586,106331,160418,295806,314853,368358,459825

%N 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.

%C Presumably there are infinitely many such triples.

%H Rémy Sigrist, <a href="/A071711/b071711.txt">Table of n, a(n) for n = 1..90</a>

%H K. S. Brown, <a href="http://www.mathpages.com/home/kmath059.htm">Sequences With No Arithmetic Progressions</a>

%H Rémy Sigrist, <a href="/A071711/a071711.txt">C++ program</a>

%o (C++) See Links section.

%Y Cf. A005839.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Jun 03 2002

%E More terms from _Rémy Sigrist_, Mar 14 2023