A241493 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

Offset

1,1

Comments

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

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Example

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.

Maple

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);

Mathematica

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

Crossrefs

Cf. A072381, A082919, A241483, A241484.

Sequence in context: A345968 A186846 A198510 * A328452 A202985 A063891

Adjacent sequences: A241490 A241491 A241492 * A241494 A241495 A241496

Keyword

nonn

Author

K. D. Bajpai, Apr 24 2014

Status

approved