OFFSET
1,1
COMMENTS
Equivalently odd prime numbers p in increasing order such that p is of the form 2q^h - 1 for some odd prime number q and some positive integer h >= 1.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
For n = 5 one has a(5) = 53 since a(1) = 5, a(2) = 13, a(3) = 17, a(4) = 37 and 53 = 2 * 3^3 - 1 is the smallest prime p > 37 of the form p = 2 * q^h - 1, with q an odd prime and h >= 1 a positive integer.
MAPLE
with(numtheory):
a:= proc(n) option remember; local l, p;
p:= `if`(n=1, 2, a(n-1));
do p:= nextprime(p);
l:= ifactors(sigma(p)/2)[2];
if nops(l)=1 and l[1][1]<>2 then break fi
od; p
end:
seq(a(n), n=1..60); # Alois P. Heinz, Apr 22 2011
MATHEMATICA
selQ[p_] := Module[{s, f}, s = DivisorSigma[1, p]/2; f = FactorInteger[s]; Length[f] == 1 && f[[1, 1]] > 2]; Select[Prime /@ Range[2, 400], selQ] (* Jean-François Alcover, Nov 22 2013 *)
PROG
(PARI) is(n)=isprime(n) && n>4 && n%4==1 && isprimepower((n+1)/2) \\ Charles R Greathouse IV, Nov 22 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Luis H. Gallardo, Apr 21 2011
EXTENSIONS
Simpler name from Charles R Greathouse IV, Nov 22 2013
STATUS
approved