A215684 Let p=prime=a(n); then a(n+1) = smallest prime q>p such that 2p+q and 2q+p are both primes.

3, 5, 7, 17, 67, 107, 277, 353, 487, 557, 787, 797, 853, 983, 1033, 1163, 1597, 1637, 1657, 1697, 1867, 1913, 2347, 2543, 2833, 2897, 2953, 2957, 3343, 3413, 3607, 3623, 3643, 3863, 3907, 4013, 4447, 4583, 4987, 5087, 5113, 5507, 6277, 6653, 7027, 7433, 7603

Offset

1,1

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Example

2*3+5=11 and 2*5+3=13 are both prime, so a(2) = 5.
2*7+17=31 and 2*17+7=41 are both prime, so a(4) = 17.

Mathematica

a=3; s={a}; m=100; Do[n1=PrimePi[a]+1; Do[b=Prime[n]; If[PrimeQ[2*a+b]&&PrimeQ[2*b+a], AppendTo[s, b]; a=b; Break[]], {n, n1, n1+100000}], {m-1}]; s
spq[n_]:=Module[{p=NextPrime[n]}, While[!PrimeQ[2n+p]||!PrimeQ[2p+n], p=NextPrime[p]]; p]; NestList[spq, 3, 50] (* Harvey P. Dale, Apr 06 2019 *)

Crossrefs

Cf. A181848.

Sequence in context: A075227 A350880 A345529 * A229132 A270779 A350176

Adjacent sequences: A215681 A215682 A215683 * A215685 A215686 A215687

Keyword

nonn

Author

Zak Seidov, Aug 20 2012

Status

approved