A351332 Primes congruent to 1 (mod 3) that divide some Fermat number.

274177, 319489, 6700417, 825753601, 1214251009, 6487031809, 646730219521, 6597069766657, 25409026523137, 31065037602817, 46179488366593, 151413703311361, 231292694251438081, 1529992420282859521, 2170072644496392193, 3603109844542291969

Offset

1,1

Comments

Subsequence of A014752.

References

Allan Cunningham, Haupt-exponents of 2, The Quarterly Journal of Pure and Applied Mathematics, Vol. 37 (1906), pp. 122-145.

Links

Table of n, a(n) for n=1..16.

Wilfrid Keller, Prime factors k.2^n + 1 of Fermat numbers F_m.

Formula

A002476 INTERSECT A023394.

Example

a(1) = 503^2 + 27*28^2 = 274177 is a prime factor of 2^(2^6) + 1;
a(2) = 383^2 + 27*80^2 = 319489 is a prime factor of 2^(2^11) + 1;
a(3) = 887^2 + 27*468^2 = 6700417 is a prime factor of 2^(2^5) + 1;
a(4) = 27017^2 + 27*1884^2 = 825753601 is a prime factor of 2^(2^16) + 1;
a(5) = 2561^2 + 27*6688^2 = 1214251009 is a prime factor of 2^(2^15) + 1;

Prog

(PARI) isok(p) = if(p%6==1 && isprime(p), my(z=znorder(Mod(2, p))); z>>valuation(z, 2)==1, return(0));

Crossrefs

Cf. A002476, A014752, A023394, A204620, A229850, A229853.

Sequence in context: A151650 A128479 A098786 * A235300 A256364 A250509

Adjacent sequences: A351329 A351330 A351331 * A351333 A351334 A351335

Keyword

nonn

Author

Arkadiusz Wesolowski, Feb 07 2022

Status

approved