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%I #8 Jun 03 2014 09:13:29
%S 11,17,41,79,199,307,331,349,379,613,643,661,673,701,769,877,883,947,
%T 1049,1249,1279,1301,1319,1381,1423,1483,1543,1559,1609,1667,1699,
%U 1759,1777,1801,1831,1871,1993,2011,2083,2347,2539,2621,2671,2687,2777,2833,2861
%N Primes p such that p^3 - 2 and p^2 - 2 are both semiprimes.
%C Similar sequence for primes is A242979.
%C Intersection of A241716 and A242260.
%H K. D. Bajpai, <a href="/A243222/b243222.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%e 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.
%p 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);
%t A243222 = {}; Do[t = Prime[n]; If[PrimeOmega[t^3 - 2] == 2 && PrimeOmega[t^2 - 2] == 2, AppendTo[A243222, t]], {n, 1000}]; A243222
%o (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
%Y Cf. A000040, A001358, A062326, A241716, A242260, A241732, A178251, A242979.
%K nonn
%O 1,1
%A _K. D. Bajpai_, Jun 01 2014
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