A257718 a(n) = smallest prime not included earlier such that a(n) + a(n-1) + a(n-2) is a prime and is of opposite index parity to a(n-1), beginning with a(1) = 3 and a(2) = 5.

3, 5, 29, 67, 7, 23, 13, 11, 19, 17, 37, 47, 43, 41, 53, 73, 71, 83, 79, 31, 89, 59, 163, 109, 101, 97, 113, 103, 61, 149, 107, 127, 139, 167, 151, 191, 181, 137, 131, 211, 199, 197, 173, 277, 193, 257, 223, 179, 229, 233, 239, 367, 251, 241, 281, 307, 271, 389, 293, 157

Offset

1,1

Comments

Is a rearrangement of A065091.

Another sequence can be created by reversing the beginning two terms. It would begin: 5, 3, 11, 29, 31, 7, 23, 13, 17, 37, ..., .

A third sequence could have a(1) = 5 and a(2) = 11 (motivated from A257717). The sequence starts: 5, 11, 3, 17, 53, 31, 13, 23, 7, 41 ... . Do any two initial odd primes generate a rearrangement of A065091? - Derek Orr, May 13 2015

Links

Table of n, a(n) for n=1..60.

Example

a(3) = 29 since a(1)+a(2) is 8 and 29 whose index is 10 and is of opposite parity to 5, whose index being 3 is odd, is the first prime which meets the criteria. 8 + 11 = 19, a prime see A073653(3), but the prime index of 11 is 5 and is of the same parity as the prime index of 5 and therefore cannot be used.

Mathematica

f[s_List] := Block[{p = s[[-2]] + s[[-1]], q = NextPrime[2, Mod[PrimePi@ s[[-1]], 2]]}, While[ !PrimeQ[p + q] || MemberQ[s, q], q = NextPrime[q, 2]]; Append[s, q]]; Nest[f, {3, 5}, 58]

Prog

(PARI) v=[3, 5]; n=1; while(n<100, p=prime(n); if((primepi(v[#v])-n)%2&&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, A257717.

Sequence in context: A303971 A136085 A153413 * A132281 A048637 A128551

Adjacent sequences: A257715 A257716 A257717 * A257719 A257720 A257721

Keyword

nonn

Author

Robert G. Wilson v, May 05 2015

Status

approved