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%I A241493 #10 Nov 28 2017 13:39:35
%S A241493 1627,2917,3583,4603,5581,6367,6379,8263,9697,12517,12763,13339,14197,
%T A241493 15289,16339,16993,17539,17737,18199,19267,19531,20023,28057,28879,
%U A241493 29587,32647,33427,34033,34537,35353,35617,37039,37087,37657,37663,42337,43093,47533,48049
%N A241493 Primes p such that p + 4, p + 16, p + 64, p + 256 and p + 1024 are all semiprimes.
%C A241493 The constants in the definition (4, 16, 64, 256 and 1024 ) are in geometric progression.
%H A241493 K. D. Bajpai, <a href="/A241493/b241493.txt">Table of n, a(n) for n = 1..10000</a>
%e A241493 1627 is prime and appears in the sequence because 1627+4 = 1631 = 7*233, 1627+16 = 1643 = 31*53, 1627+64 = 1691 = 19*89, 1627+256 = 1883 = 7*269 and 1627+1024 = 2651 = 11*241, which are all semiprime.
%p A241493 with(numtheory): KD:= proc() local a,b,d,e,f,k; k:=ithprime(n); a:=bigomega(k+4); b:=bigomega(k+16); d:=bigomega(k+64); e:=bigomega(k+256); f:=bigomega(k+1024); if a=2 and  b=2 and d=2 and  e=2 and f=2 then RETURN (k); fi; end: seq(KD(), n=1..10000);
%t A241493 KD = {}; Do[t = Prime[n]; If[PrimeOmega[t + 4] == 2 && PrimeOmega[t + 16] == 2 && PrimeOmega[t + 64] == 2 && PrimeOmega[t + 256] == 2 && PrimeOmega[t + 1024] == 2, AppendTo[KD, t]], {n, 10000}]; KD
%t A241493 (* For the b-file *) c = 0; Do[t = Prime[n]; If[PrimeOmega[t + 4] == 2 && PrimeOmega[t + 16] == 2 && PrimeOmega[t + 64] == 2 && PrimeOmega[t + 256] == 2 && PrimeOmega[t + 1024] == 2, c++; Print[c, "  ", t]], {n, 1,5*10^6}];
%t A241493 Select[Prime[Range[5000]],Union[PrimeOmega[#+{4,16,64,256,1024}]] == {2}&] (* _Harvey P. Dale_, Nov 28 2017 *)
%Y A241493 Cf. A072381, A082919, A241483, A241484.
%K A241493 nonn
%O A241493 1,1
%A A241493 _K. D. Bajpai_, Apr 24 2014

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