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Sorted list of prime factors of numbers of the form 3^(2^m) + 2^(2^m) with m >= 0.
7

%I #17 Jul 29 2019 11:52:33

%S 5,13,17,97,257,401,769,1153,3041,14177,65537,286721,1810433,2752513,

%T 4043777,7340033,13631489,23068673,72222721,319291393,348061697,

%U 625483777,3937533953,54498164737,106216554497,121899667073,151597350913,342456532993

%N Sorted list of prime factors of numbers of the form 3^(2^m) + 2^(2^m) with m >= 0.

%C Primes p such that the multiplicative order of 3/2 (mod p) is a power of 2.

%H Arkadiusz Wesolowski, <a href="/A294132/b294132.txt">Table of n, a(n) for n = 1..48</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.

%e The first 5 such numbers are 5, 13, 97, 6817, 43112257, 1853024483819137. Their prime factorizations are (5), (13), (97), (17) (401), (14177) (3041), (1153) (1607133116929). - _N. J. A. Sloane_, Oct 29 2017

%o (PARI) print1(5, ", "); forprime(p=13, 342456532993, z=znorder(Mod(3/2, p)); if(2^ispower(z)==z, print1(p, ", ")));

%Y Cf. A050244, A094499, A082101, A294133, A294134, A294135, A294136.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Oct 23 2017