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A275528
Prime factors of numbers of the form 4^(2^m) - 2^(2^m) + 1 with m >= 0.
3
3, 13, 97, 193, 241, 673, 769, 12289, 786433, 22253377, 39714817, 152371201, 597688321, 1107296257, 3221225473, 7348420609, 11560943617, 29796335617, 74490839041, 77309411329, 206158430209, 246423748609, 448203325441, 2422022479873, 5469640851457, 28114855919617
OFFSET
1,1
COMMENTS
Primes p other than 3 such that one third of the multiplicative order of 2 (mod p) is a power of 2.
Primes in A255772 (except 7), sorted.
LINKS
Arkadiusz Wesolowski, Table of n, a(n) for n = 1..27
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.
EXAMPLE
3 divides 2^2 - 2^1 + 1 = 3.
13 divides 2^4 - 2^2 + 1 = 13.
97 divides 2^16 - 2^8 + 1 = 65281.
193 divides 2^32 - 2^16 + 1 = 4294901761.
241 divides 2^8 - 2^4 + 1 = 241.
673 divides 2^16 - 2^8 + 1 = 65281.
769 divides 2^128 - 2^64 + 1 = 340282366920938463444927863358058659841.
12289 divides 2^2048 - 2^1024 + 1.
PROG
(PARI) forprime(p=3, 10^15, o=znorder(Mod(2, p))/3; x=ispower(2*o); if(p==3||2^(x-1)==o, print1(p, ", ")));
CROSSREFS
Sequence in context: A277492 A374231 A342305 * A129375 A293528 A228160
KEYWORD
nonn
AUTHOR
STATUS
approved