Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Jul 23 2021 05:25:37
%S 2,119,372,814,4350,9797,16625,16729,40224,45191,48121,63137,71520,
%T 83264,89744,94166,103551,109538,111283,113690,117620,232363,265101,
%U 268661,269466,302024,316847,329793,333947,334725,340910,352997,380914,381169,384459,385927
%N Numbers k such that 2*prime(k)+1, 2*prime(k+1)+1 and 2*prime(k+2)-1 are also consecutive primes.
%H Amiram Eldar, <a href="/A103851/b103851.txt">Table of n, a(n) for n = 1..10000</a>
%e 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).
%t 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 *)
%Y Cf. A103852.
%K nonn
%O 1,1
%A _Pierre CAMI_, Feb 18 2005
%E Corrected by _T. D. Noe_, Nov 02 2006
%E a(21) and a(30) inserted and a(36) added by _Amiram Eldar_, Jul 23 2021