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%I #10 Nov 29 2019 04:02:12
%S 13,587,1361,15227,118967,337721,383267,512891,1027331,1780151,
%T 2303681,8200391,9310517,14666579,25005089,29105981,34824971,38895497,
%U 40436909,51819461,63462977,65427749,65599199,66043091,75552479,94671671
%N Chen primes p such that their p + 2 counterpart is a golden semiprime.
%C Conjecture: sequence is infinite.
%H Amiram Eldar, <a href="/A109875/b109875.txt">Table of n, a(n) for n = 1..10000</a>
%e 1361 is a term because it is prime and 1363 = 29*47 and abs(29*phi - 47) = 0.07701... < 1.
%t f[p_] := Module[{x = GoldenRatio * p}, p1 = NextPrime[x, -1]; p2 = NextPrime[p1]; q = If[x - p1 < p2 - x, p1, p2]; If[Abs[q - x] < 1, q, 0]]; seq = {}; p = 1; Do[p = NextPrime[p]; q = f[p]; If[q > 0 && PrimeQ[p*q - 2], AppendTo[seq, p*q - 2]], {1000}]; seq (* _Amiram Eldar_, Nov 29 2019 *)
%Y Cf. A109611, A108540.
%K nonn
%O 1,1
%A _Jason Earls_, Aug 31 2005
%E a(15)-a(26) from _Donovan Johnson_, Nov 17 2008
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