

A273948


Odd prime factors of generalized Fermat numbers of the form 7^(2^m) + 1 with m >= 0.


8



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

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  p1. 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)


REFERENCES

Hans Riesel, Common prime factors of the numbers A_n=a^(2^n)+1, BIT 9 (1969), pp. 264269.


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. 441446.
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. 18651866.
Harvey Dubner and Wilfrid Keller, Factors of Generalized Fermat Numbers, Math. Comp. 64 (1995), no. 209, pp. 397405.
OEIS Wiki, Generalized Fermat numbers


MAPLE

filter:= proc(t)
if not isprime(t) then return false fi;
7 &^ (2^padic:ordp(t1, 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

Cf. A023394, A072982, A078304, A273945 (base 3), A273946 (base 5), A273947 (base 6), A273949 (base 11), A273950 (base 12).
Sequence in context: A077718 A235461 A271660 * A271657 A273999 A222008
Adjacent sequences: A273945 A273946 A273947 * A273949 A273950 A273951


KEYWORD

nonn


AUTHOR

Arkadiusz Wesolowski, Jun 05 2016


STATUS

approved



