cp's OEIS Frontend

A263581 Prime powers (p^k, p prime, k >= 1) such that k*p^k - 1 is also a power of a prime.

%I A263581 #41 Apr 11 2016 03:49:39
%S A263581 2,3,4,5,8,9,17,25,49,64,121,169,257,289,729,841,1681,1849,3481,5329,
%T A263581 11881,12769,16129,18769,24649,32041,32761,38809,39601,44521,59049,
%U A263581 63001,65537,69169,76729,85849,96721,124609,134689,143641,167281,175561,187489
%N A263581 Prime powers (p^k, p prime, k >= 1) such that k*p^k - 1 is also a power of a prime.
%C A263581 Of course 1 = p^0 for any prime p, so 1 is definitely the power of a prime (comment in A000961).
%C A263581 Only primes of the form 2^m + 1 (2 and Fermat primes) are terms.
%e A263581 8 is in this sequence because both 8 = 2^3 and 3*2^3 - 1 = 23 is prime power.
%o A263581 (PARI) ispp(n) = if ((n==1) || isprime(n), return (1), isprimepower(n));
%o A263581 isok(n) = ((k=ispp(n)) && ispp(k*n-1)); \\ _Michel Marcus_, Apr 11 2016
%Y A263581 Cf. A000961, A019434 (Fermat primes), A092506 (primes of the form 2^m + 1).
%K A263581 nonn
%O A263581 1,1
%A A263581 _Juri-Stepan Gerasimov_, Apr 09 2016