cp's OEIS Frontend

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 A071711 #14 Mar 14 2023 17:24:43
%S A071711 0,7,14,28,48,55,64,86,108,168,286,371,471,633,760,982,1032,1136,1261,
%T A071711 1600,1739,1788,1822,1848,3832,4225,5504,7729,8062,9229,10110,21977,
%U A071711 27953,39335,50820,50852,86357,95586,106331,160418,295806,314853,368358,459825
%N 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.
%C A071711 Presumably there are infinitely many such triples.
%H A071711 Rémy Sigrist, <a href="/A071711/b071711.txt">Table of n, a(n) for n = 1..90</a>
%H A071711 K. S. Brown, <a href="http://www.mathpages.com/home/kmath059.htm">Sequences With No Arithmetic Progressions</a>
%H A071711 Rémy Sigrist, <a href="/A071711/a071711.txt">C++ program</a>
%o A071711 (C++) See Links section.
%Y A071711 Cf. A005839.
%K A071711 nonn
%O A071711 1,2
%A A071711 _Benoit Cloitre_, Jun 03 2002
%E A071711 More terms from _Rémy Sigrist_, Mar 14 2023