A103851 Numbers k such that 2*prime(k)+1, 2*prime(k+1)+1 and 2*prime(k+2)-1 are also consecutive primes.

2, 119, 372, 814, 4350, 9797, 16625, 16729, 40224, 45191, 48121, 63137, 71520, 83264, 89744, 94166, 103551, 109538, 111283, 113690, 117620, 232363, 265101, 268661, 269466, 302024, 316847, 329793, 333947, 334725, 340910, 352997, 380914, 381169, 384459, 385927

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

2*3+1 = 5, 2*5+1 = 7, 2*7 - 1 = 13; 3, 5 and 7 are consecutive primes as are 5, 7 and 13, so a(1) = 2 as 3 = prime(2).

Mathematica

s={}; n=1; p1=2; p2=3; Do[p3 = NextPrime[p2]; If[PrimeQ[2*p1+1] && (np = NextPrime[2*p1+1]) == 2*p2+1 && NextPrime[np] == 2*p3-1, AppendTo[s, n]]; p1=p2; p2=p3; n++, {10^5}]; s (* Amiram Eldar, Jul 23 2021 *)

Crossrefs

Cf. A103852.

Sequence in context: A013511 A013507 A013476 * A024030 A221231 A243512

Adjacent sequences: A103848 A103849 A103850 * A103852 A103853 A103854

Keyword

nonn

Author

Pierre CAMI, Feb 18 2005

Extensions

Corrected by T. D. Noe, Nov 02 2006

a(21) and a(30) inserted and a(36) added by Amiram Eldar, Jul 23 2021

Status

approved