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A283527 First of three consecutive Sophie Germain semiprimes: n, n+1 and n+2 are all terms of A111153.

%I A283527 #8 Mar 10 2017 09:22:21
%S A283527 15117,17245,34413,93453,143101,157713,190621,208293,233097,294301,
%T A283527 323281,346497,470341,501477,1306113,1337221,1346401,1655853,1682313,
%U A283527 1774801,1877613,1879021,1933233,1976041
%N A283527 First of three consecutive Sophie Germain semiprimes: n, n+1 and n+2 are all terms of A111153.
%C A283527 All terms are 1 mod 4, see A056809.
%H A283527 Zak Seidov, <a href="/A283527/b283527.txt">Table of n, a(n) for n = 1..408</a>
%t A283527   po[x_] := PrimeOmega[x];   Select[Range[15117, 200000, 2],
%t A283527 2 == po[#] == po[2*# + 1] ==po[# + 1] == po[2*# + 3] == po[# + 2] ==
%t A283527 po[2*# + 5] &]
%o A283527 (PARI) {bo(x)=bigomega(x)
%o A283527 forstep(n=15117,2000000,2, if(
%o A283527 2 == bo(n) && 2 == bo(n+1) && 2 == bo(n+2) && 2 == bo(2*n+1) &&
%o A283527 2 == bo(2*n+3) && 2 == bo(2*n+5), print1(n",")))}
%o A283527 (PARI) list(lim)=lim\=1; my(v=List(),x=2*lim+5,u=vectorsmall(x)); forprime(p=2,x\2, forprime(q=2,min(lim\p,p), u[p*q]=1)); forstep(n=15117,lim,4, if(u[n] && u[n+1] && u[n+2] && u[2*n+1] && u[2*n+3] && u[2*n+5], listput(v,n))); Vec(v) \\ _Charles R Greathouse IV_, Mar 10 2017
%Y A283527 Subsequence of A056809 and of A111153. Cf. A001358.
%K A283527 nonn
%O A283527 1,1
%A A283527 _Zak Seidov_, Mar 09 2017