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A131741 a(n) is least prime (not already in list) such that no 3-term subset forms an arithmetic progression.

%I A131741 #14 Oct 30 2019 16:26:06
%S A131741 2,3,5,11,13,29,31,37,41,67,73,83,89,101,107,127,139,157,179,193,227,
%T A131741 233,263,271,281,307,331,337,379,389,397,401,409,431,433,467,491,499,
%U A131741 509,563,571,613,641,647,743,769,809,823,883,887,907,937,983,1009,1021
%N A131741 a(n) is least prime (not already in list) such that no 3-term subset forms an arithmetic progression.
%C A131741 a(n) is the smallest prime such that there is no i < j < n with a(n) - a(j) = a(j) - a(i).
%H A131741 Vincenzo Librandi, <a href="/A131741/b131741.txt">Table of n, a(n) for n = 1..1000</a>
%H A131741 <a href="http://oeis.org/wiki/Index_to_OEIS:_Section_No#non_averaging">Index entries for non-averaging sequences</a>
%e A131741 Table showing derivation of first 10 values.
%e A131741 n a(n) comment
%e A131741 1 2
%e A131741 2 3
%e A131741 3 5
%e A131741 4 11 a(4) can't be 7 because (3,5,7) is in arithmetic progression.
%e A131741 5 13
%e A131741 6 29 a(6) can't be 17 because (5,11,17); can't be 19 because (3,11,19); can't be 23 because (3,13,23)
%e A131741 7 31
%e A131741 8 37
%e A131741 9 41
%e A131741 10 67 a(10) not 43 as (31,37,43); not 47 as (11,29,47); not 53 as (29,41,53); not 59 as (13,31,59); not 61 as (13,37,61)
%t A131741 f[l_List] := Block[{c, f = 0}, c = If[l == {}, 0, l[[ -1]]]; While[f == 0, c = NextPrime[c]; If[Intersection[l, l - (c - l)] == {}, f = 1]; ]; Append[l, c] ]; Nest[f, {}, 100] (* _Ray Chandler_, Oct 06 2007 *)
%o A131741 (PARI) nxt(v)=my(t); forprime(p=v[#v]+1,,forstep(i=#v,3,-1,t=2*v[i]-p; if(t<3, if(i==#v,break,next)); if(setsearch(v,t),next(2))); return(p))
%o A131741 list(n)=my(v=[2]);for(k=2,n,v=concat(v,nxt(v))); v \\ _Charles R Greathouse IV_, Jan 30 2014
%Y A131741 Cf. A000040, A065825.
%K A131741 easy,nonn
%O A131741 1,1
%A A131741 _Jonathan Vos Post_, Oct 04 2007
%E A131741 More terms from _Ray Chandler_, Oct 06 2007.