cp's OEIS Frontend

A257717 a(n) is the smallest odd-indexed prime not included earlier such that a(n) + a(n-1) + a(n-2) is a prime, beginning with a(1) = 5 and a(2) = 11.

%I A257717 #22 Mar 23 2024 12:20:41
%S A257717 5,11,31,17,23,67,41,59,73,47,103,83,97,127,149,157,137,167,283,191,
%T A257717 179,109,211,227,313,233,197,331,241,257,379,347,307,367,389,277,353,
%U A257717 401,439,269,509,499,419,449,571,431,487,563,461,547,523,587,599,661,607,761,631,677
%N A257717 a(n) is the smallest odd-indexed prime not included earlier such that a(n) + a(n-1) + a(n-2) is a prime, beginning with a(1) = 5 and a(2) = 11.
%C A257717 Conjecture: The union of this sequence and A257716 is A065091.
%e A257717 a(3) = 31 since a(1)+a(2) is 16 and 31, whose index equals 11, is the first odd-indexed prime which meets the criteria. 16 + 7 = 23, a prime, but 7 is the 4th prime and therefore cannot be used.
%t A257717 f[s_List] := Block[{p = s[[-2]] + s[[-1]], q = 17}, While[ !PrimeQ[p + q] || MemberQ[s, q], q = NextPrime[q, 2]]; Append[s, q]]; Nest[f, {5, 11}, 56]
%o A257717 (PARI) v=[5,11];n=1;while(n<100,p=prime(2*n-1);if(isprime(v[#v]+v[#v-1]+p)&&!vecsearch(vecsort(v),p),v=concat(v,p);n=0);n++);v \\ _Derek Orr_, May 13 2015
%Y A257717 Cf. A031368, A073653, A257716, A257718.
%K A257717 nonn
%O A257717 1,1
%A A257717 _Robert G. Wilson v_, May 05 2015