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

Author

Zak Seidov, Aug 20 2012

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A181848.

Programs

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 *)