A243222 Primes p such that p^3 - 2 and p^2 - 2 are both semiprimes.

11, 17, 41, 79, 199, 307, 331, 349, 379, 613, 643, 661, 673, 701, 769, 877, 883, 947, 1049, 1249, 1279, 1301, 1319, 1381, 1423, 1483, 1543, 1559, 1609, 1667, 1699, 1759, 1777, 1801, 1831, 1871, 1993, 2011, 2083, 2347, 2539, 2621, 2671, 2687, 2777, 2833, 2861

Offset

1,1

Comments

Similar sequence for primes is A242979.

Intersection of A241716 and A242260.

Links

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

Example

11 is prime and appears in the sequence because [ 11^3 - 2 = 1329 = 3 * 443 ] and [ 11^2 - 2 = 119 = 7 * 17 ] are both semiprimes.
17 is prime and appears in the sequence because [ 17^3 - 2 = 4911 = 3 * 1637 ] and [ 17^2 - 2 = 287 = 7 * 41 ] are both semiprimes.

Maple

with(numtheory): A243222:= proc() local p; p:=ithprime(n); if bigomega(p^3-2)=2 and bigomega(p^2-2) =2 then RETURN (p);  fi; end: seq( A 243222 (), n=1..1000);

Mathematica

A243222 = {}; Do[t = Prime[n]; If[PrimeOmega[t^3 - 2] == 2 && PrimeOmega[t^2 - 2] == 2, AppendTo[A243222, t]], {n, 1000}]; A243222

Prog

(PARI) s=[]; forprime(p=2, 3000, if(bigomega(p^2-2)==2 && bigomega(p^3-2)==2, s=concat(s, p))); s \\ Colin Barker, Jun 03 2014

Crossrefs

Cf. A000040, A001358, A062326, A241716, A242260, A241732, A178251, A242979.

Sequence in context: A267291 A073649 A178070 * A090609 A187057 A187058

Adjacent sequences: A243219 A243220 A243221 * A243223 A243224 A243225

Keyword

nonn

Author

K. D. Bajpai, Jun 01 2014

Status

approved