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 #13 Feb 03 2017 21:46:31
%S 10193,12113,17683,19501,63743,70793,74317,74797,79657,89231,109073,
%T 112657,114371,116993,119237,120431,130211,139801,148573,152123,
%U 164881,173867,201623,230017,264919,275543,284927,290761,323537,325643,371873,382777,385193,396061,399403,402817,415201,421273
%N Primes p such that, for p < q < r three consecutive primes, p + 2q + 2r, 2p + q + 2r and 2p + 2q + r are all primes.
%C From first 10^5 primes, only 92 are terms. Indices of primes are 1252, 1451, 2032,..., 95460, 97950, 98973.
%C Note that p == q == r (mod 6), e.g., {10193, 10211, 10223} == 5 mod 6 and {17683, 17707, 17713} == 1 mod 6.
%H Harvey P. Dale, <a href="/A216262/b216262.txt">Table of n, a(n) for n = 1..1000</a>
%e a(1) = p = 10193; s = {p, q, r} = {10193, 10211, 10223};
%e {{1,2,2}.s, {2,1,2}.s, {2,2,1}.s} = {51061, 51043, 51031} all primes.
%t pr=Partition[Prime[Range[40000]],3,1]; Reap[Do[s=pr[[k]]; If[Union[PrimeQ[{{1,2,2}.s,{2,1,2}.s,{2,2,1}.s}]]=={True},Sow[Prime[k]]],{k,Length[pr]}]][[2,1]]
%t tcpQ[{p_,q_,r_}]:=AllTrue[{p+2q+2r,2p+q+2r,2p+2q+r},PrimeQ]; Select[ Partition[ Prime[Range[36000]],3,1],tcpQ][[All,1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Feb 03 2017 *)
%K nonn
%O 1,1
%A _Zak Seidov_, Mar 15 2013