

A193051


Primes p such that 12*p^21 and 16*p^31 are also primes.


1



2, 3, 17, 29, 107, 167, 173, 599, 1667, 1889, 2129, 3407, 3539, 3797, 3863, 5189, 6779, 6983, 7529, 8849, 11399, 11519, 11657, 12227, 12437, 12809, 13217, 14153, 15227, 16223, 16607, 17609, 21683, 21863, 22193, 23789, 25127
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OFFSET

1,1


COMMENTS

Primes p such that 3*(2p)^21 (see A089681) and 2*(2p)^31 are primes.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000


EXAMPLE

For p=2, 2 is a prime number, 12*2^21=47 is a prime number and 16*2^31=127 is a prime number.
For p=3, 3 is a prime number, 12*3^21=109 is a prime number and 16*3^31=431 is a prime number.


MATHEMATICA

fQ[n_] := PrimeQ[12 n^2  1] && PrimeQ[16 n^3  1]; Select[ Prime@ Range@ 3000, fQ] (* Robert G. Wilson v, Aug 08 2011 *)
Select[Prime[Range[5000]], PrimeQ[12 #^2  1] && PrimeQ[16 #^3  1]&] (* Vincenzo Librandi, Apr 10 2013 *)


PROG

(MAGMA) [p: p in PrimesUpTo(26000)IsPrime(12*p^21) and IsPrime(16*p^31)]; // Vincenzo Librandi, Apr 10 2013


CROSSREFS

Cf. A158463.
Sequence in context: A215303 A215280 A219559 * A217688 A263570 A029733
Adjacent sequences: A193048 A193049 A193050 * A193052 A193053 A193054


KEYWORD

nonn,easy


AUTHOR

JuriStepan Gerasimov, Jul 15 2011


STATUS

approved



