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 A257716 a(n) = smallest prime of even index not included earlier such that a(n) + a(n-1) + a(n-2) is a prime, beginning with a(1) = 3 and a(2) = 7. 3
 3, 7, 13, 53, 37, 19, 71, 61, 79, 89, 29, 139, 43, 101, 107, 151, 131, 181, 229, 113, 199, 251, 163, 173, 263, 223, 271, 239, 311, 193, 293, 337, 281, 349, 317, 373, 359, 397, 457, 383, 409, 421, 491, 521, 541, 557, 433, 443, 577, 463, 503, 593, 601, 673, 479, 569, 619, 613 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The union of A257716 and A257717 is A065091 (conjecture). LINKS EXAMPLE a(4) = 53 since a(2)+a(3) is 20 and 53, whose index equals 16, is the first even-indexed prime which meets the criteria. 20 + 11 = 31, a prime, but 11 is the 5th prime and therefore cannot be used. MATHEMATICA f[s_List] := Block[{p = s[[-2]] + s[[-1]], q = 13}, While[ !PrimeQ[p + q] || MemberQ[s, q], q = NextPrime[q, 2]]; Append[s, q]]; Nest[f, {3, 7}, 56] PROG (PARI) v=[3, 7]; n=1; while(n<100, if(isprime(v[#v]+v[#v-1]+prime(2*n))&&!vecsearch(vecsort(v), prime(2*n)), v=concat(v, prime(2*n)); n=0); n++); v \\ Derek Orr, May 13 2015 CROSSREFS Cf. A073653, A257717, A257718. Sequence in context: A090968 A020641 A062736 * A103564 A083201 A228209 Adjacent sequences:  A257713 A257714 A257715 * A257717 A257718 A257719 KEYWORD nonn AUTHOR Robert G. Wilson v, May 05 2015 STATUS approved

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Last modified April 8 14:52 EDT 2020. Contains 333314 sequences. (Running on oeis4.)