A241659 Primes p such that p^3 + 2 is semiprime.
2, 11, 13, 17, 19, 23, 31, 41, 53, 59, 89, 101, 131, 137, 149, 193, 211, 223, 227, 229, 233, 239, 251, 271, 293, 317, 331, 359, 401, 449, 461, 557, 563, 571, 593, 599, 619, 641, 659, 677, 691, 719, 739, 751, 809, 821, 853, 929, 971, 991, 1009, 1013, 1039, 1051
Offset: 1
Keywords
Examples
11 is prime and appears in the sequence because 11^3 + 2 = 1333 = 31 * 43, which is a semiprime. 17 is prime and appears in the sequence because 17^3 + 2 = 4915 = 5 * 983, which is a semiprime. 37 is prime but does not appear in the sequence because 37^3 + 2 = 50655 = 3 * 5 * 11 * 983, which is not a semiprime.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..10000
Programs
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Maple
with(numtheory): KD:= proc() local a, b, k; k:=ithprime(n); a:=bigomega(k^3+2); if a=2 then RETURN (k); fi; end: seq(KD(), n=1..500);
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Mathematica
A241659 = {}; Do[t = Prime[n]; If[PrimeOmega[t^3 + 2] == 2, AppendTo[A241659, t]], {n, 500}]; A241659 (*For the b-file*) c = 0; Do[t = Prime[n]; If[PrimeOmega[t^3 + 2] == 2, c++; Print[c, " ", t]], {n, 1,6*10^4}]; Select[Prime[Range[200]],PrimeOmega[#^3+2]==2&] (* Harvey P. Dale, Feb 05 2025 *)
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PARI
s=[]; forprime(p=2, 1200, if(bigomega(p^3+2)==2, s=concat(s, p))); s \\ Colin Barker, Apr 27 2014