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
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Apr 24 2014
STATUS
approved