|
|
A125739
|
|
Primes p such that 3^p + 3^((p + 1)/2) + 1 is prime.
|
|
4
|
|
|
3, 5, 7, 17, 19, 79, 163, 317, 353, 1049, 1759, 5153, 7541, 23743, 2237561, 4043119
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
PrimePi[ a(n) ] = {2, 3, 4, 7, 8, 22, 38, 66, 71, 176, 274, 687, 956, ...}, the indices of the primes p.
|
|
LINKS
|
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
|
|
MATHEMATICA
|
Do[p=Prime[n]; f=3^p+3^((p+1)/2)+1; If[PrimeQ[f], Print[{n, p}]], {n, 1, 200}]
|
|
PROG
|
(PARI) lista(nn) = {forprime(p=3, nn, if (ispseudoprime(3^p + 3^((p + 1)/2) + 1), print1(p, ", ")); ); } \\ Michel Marcus, Oct 13 2014
(Magma) [p: p in PrimesUpTo(5000) | IsPrime(3^p+3^((p+1)div 2)+1)]; // Vincenzo Librandi, Oct 13 2014
|
|
CROSSREFS
|
Cf. A125738 = Primes p such that 3^p - 3^((p + 1)/2) + 1 is prime.
Cf. A007670 = Numbers n such that 2^n - 2^((n + 1)/2) + 1 is prime.
Cf. A007671 = Numbers n such that 2^n + 2^((n + 1)/2) + 1 is prime.
Cf. A066408 = Numbers n such that the Eisenstein integer has prime norm.
|
|
KEYWORD
|
hard,more,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
a(14) from Lelio R Paula (lelio(AT)sknet.com.br), May 07 2008
|
|
STATUS
|
approved
|
|
|
|