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A273948
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Odd prime factors of generalized Fermat numbers of the form 7^(2^m) + 1 with m >= 0.
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8
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5, 17, 257, 353, 769, 1201, 12289, 13313, 35969, 65537, 114689, 163841, 169553, 7699649, 9379841, 11886593, 28667393, 64749569, 70254593, 134818753, 197231873, 4643094529, 19847446529, 47072139617, 206158430209, 452850614273, 531968664833, 943558259713
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OFFSET
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1,1
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COMMENTS
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Odd primes p other than 3 such that the multiplicative order of 7 (mod p) is a power of 2.
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.
The intersection of this sequence and A019337 is A019434 minus {3}. (End)
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REFERENCES
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Hans Riesel, Common prime factors of the numbers A_n=a^(2^n)+1, BIT 9 (1969), pp. 264-269.
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LINKS
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MAPLE
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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
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MATHEMATICA
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Select[Prime@Range[3, 10^5], IntegerQ@Log[2, MultiplicativeOrder[7, #]] &]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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