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

Author

Arkadiusz Wesolowski, Feb 07 2022

Keywords

• nonn

Comments

Subsequence of A014752.

Examples

			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;
		

References

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

Links

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

Crossrefs

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

Programs

PARI

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

Formula

A002476 INTERSECT A023394.