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Select[Prime[Range[5000]], Union[PrimeOmega[#+{4, 16, 64, 256, 1024}]] == {2}&] (* Harvey P. Dale, Nov 28 2017 *)

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Select[Prime[Range[5000]], Union[PrimeOmega[#+{4, 16, 64, 256, 1024}]]=={2}&] (* Harvey P. Dale, Nov 28 2017 *)

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K. D. Bajpai, <a href="/A241493/b241493.txt">Table of n, a(n) for n = 1..10000</a>

allocated for K. D. Bajpai

Primes p such that p + 4, p + 16, p + 64, p + 256 and p + 1024 are all semiprimes.

1627, 2917, 3583, 4603, 5581, 6367, 6379, 8263, 9697, 12517, 12763, 13339, 14197, 15289, 16339, 16993, 17539, 17737, 18199, 19267, 19531, 20023, 28057, 28879, 29587, 32647, 33427, 34033, 34537, 35353, 35617, 37039, 37087, 37657, 37663, 42337, 43093, 47533, 48049

1,1

The constants in the definition (4, 16, 64, 256 and 1024 ) are in geometric progression.

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.

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);

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

(* 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}];

Cf. A072381, A082919, A241483, A241484.

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nonn,new

K. D. Bajpai, Apr 24 2014

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allocated for K. D. Bajpai

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