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%I #16 Jun 16 2016 22:42:00
%S 5,17,257,353,769,1201,12289,13313,35969,65537,114689,163841,169553,
%T 7699649,9379841,11886593,28667393,64749569,70254593,134818753,
%U 197231873,4643094529,19847446529,47072139617,206158430209,452850614273,531968664833,943558259713
%N Odd prime factors of generalized Fermat numbers of the form 7^(2^m) + 1 with m >= 0.
%C Odd primes p other than 3 such that the multiplicative order of 7 (mod p) is a power of 2.
%C From _Robert Israel_, Jun 16 2016: (Start)
%C 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.
%C The intersection of this sequence and A019337 is A019434 minus {3}. (End)
%D Hans Riesel, Common prime factors of the numbers A_n=a^(2^n)+1, BIT 9 (1969), pp. 264-269.
%H Arkadiusz Wesolowski, <a href="/A273948/b273948.txt">Table of n, a(n) for n = 1..34</a>
%H Anders Björn and Hans Riesel, <a href="http://dx.doi.org/10.1090/S0025-5718-98-00891-6">Factors of generalized Fermat numbers</a>, Math. Comp. 67 (1998), no. 221, pp. 441-446.
%H Anders Björn and Hans Riesel, <a href="http://dx.doi.org/10.1090/S0025-5718-05-01816-8">Table errata to “Factors of generalized Fermat numbers”</a>, Math. Comp. 74 (2005), no. 252, p. 2099.
%H Anders Björn and Hans Riesel, <a href="http://dx.doi.org/10.1090/S0025-5718-10-02371-9">Table errata 2 to "Factors of generalized Fermat numbers"</a>, Math. Comp. 80 (2011), pp. 1865-1866.
%H Harvey Dubner and Wilfrid Keller, <a href="http://dx.doi.org/10.1090/S0025-5718-1995-1270618-1">Factors of Generalized Fermat Numbers</a>, Math. Comp. 64 (1995), no. 209, pp. 397-405.
%H OEIS Wiki, <a href="/wiki/Generalized_Fermat_numbers">Generalized Fermat numbers</a>
%p filter:= proc(t)
%p if not isprime(t) then return false fi;
%p 7 &^ (2^padic:-ordp(t-1,2)) mod t = 1
%p end proc:
%p select(filter, [seq(i,i=5..10^6,2)]); # _Robert Israel_, Jun 16 2016
%t Select[Prime@Range[3, 10^5], IntegerQ@Log[2, MultiplicativeOrder[7, #]] &]
%Y Cf. A023394, A072982, A078304, A273945 (base 3), A273946 (base 5), A273947 (base 6), A273949 (base 11), A273950 (base 12).
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Jun 05 2016
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