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A243222
Primes p such that p^3 - 2 and p^2 - 2 are both semiprimes.
1
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
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
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Jun 01 2014
STATUS
approved