OFFSET
1,1
COMMENTS
Odd primes p other than 3 such that the multiplicative order of 7 (mod p) is a power of 2.
From Robert Israel, Jun 16 2016: (Start)
If p is in the sequence, then for each m either p | 7^(2^k)+1 for some k < m or 2^m | p-1. Thus all members except 5, 17, 353, 1201, 169553, 7699649, 134818753, 47072139617 are congruent to 1 mod 2^7.
REFERENCES
Hans Riesel, Common prime factors of the numbers A_n=a^(2^n)+1, BIT 9 (1969), pp. 264-269.
LINKS
Arkadiusz Wesolowski, Table of n, a(n) for n = 1..34
Anders Björn and Hans Riesel, Factors of generalized Fermat numbers, Math. Comp. 67 (1998), no. 221, pp. 441-446.
Anders Björn and Hans Riesel, Table errata to “Factors of generalized Fermat numbers”, Math. Comp. 74 (2005), no. 252, p. 2099.
Anders Björn and Hans Riesel, Table errata 2 to "Factors of generalized Fermat numbers", Math. Comp. 80 (2011), pp. 1865-1866.
Harvey Dubner and Wilfrid Keller, Factors of Generalized Fermat Numbers, Math. Comp. 64 (1995), no. 209, pp. 397-405.
OEIS Wiki, Generalized Fermat numbers
MAPLE
filter:= proc(t)
if not isprime(t) then return false fi;
7 &^ (2^padic:-ordp(t-1, 2)) mod t = 1
end proc:
select(filter, [seq(i, i=5..10^6, 2)]); # Robert Israel, Jun 16 2016
MATHEMATICA
Select[Prime@Range[3, 10^5], IntegerQ@Log[2, MultiplicativeOrder[7, #]] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Arkadiusz Wesolowski, Jun 05 2016
STATUS
approved