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 A257717 a(n) is the smallest oldd-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. 3
 5, 11, 31, 17, 23, 67, 41, 59, 73, 47, 103, 83, 97, 127, 149, 157, 137, 167, 283, 191, 179, 109, 211, 227, 313, 233, 197, 331, 241, 257, 379, 347, 307, 367, 389, 277, 353, 401, 439, 269, 509, 499, 419, 449, 571, 431, 487, 563, 461, 547, 523, 587, 599, 661, 607, 761, 631, 677 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The union of A257716 and A257717 is A065091 (conjecture). LINKS EXAMPLE 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. MATHEMATICA 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] PROG (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 CROSSREFS Cf. A073653, A257716, A257718. Sequence in context: A209659 A266820 A114688 * A192194 A239842 A092963 Adjacent sequences:  A257714 A257715 A257716 * A257718 A257719 A257720 KEYWORD nonn AUTHOR Robert G. Wilson v, May 05 2015 STATUS approved

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Last modified June 4 11:32 EDT 2020. Contains 334825 sequences. (Running on oeis4.)