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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 15 03:48 EST 2019. Contains 329990 sequences. (Running on oeis4.)