A229850
Number of prime factors congruent to 1 mod 3 that divide the Fermat number 2^(2^n) + 1.
Original entry on oeis.org
0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 3, 2
Offset: 0
- M. Krizek, F. Luca, L. Somer, 17 Lectures on Fermat Numbers: From Number Theory to Geometry, CMS Books in Mathematics, vol. 9, Springer-Verlag, New York, 2001, pp. 61-63, 65-66.
A228845
Least m such that (2k+1)*2^m + 1 is a prime factor of the Fermat number 2^(2^n) + 1.
Original entry on oeis.org
1, 2, 4, 8, 16, 7, 8, 9, 11, 11, 12, 13, 14
Offset: 0
A351865
Primes of the form x^2 + 64*y^2 that divide some Fermat number.
Original entry on oeis.org
257, 65537, 2424833, 26017793, 63766529, 825753601, 1214251009, 6487031809, 2710954639361, 2748779069441, 6597069766657, 25991531462657, 76861124116481, 151413703311361, 1095981164658689, 1238926361552897, 1529992420282859521, 2663848877152141313, 3603109844542291969
Offset: 1
a(1) = 1^2 + 64*2^2 = 257 is a prime factor of 2^(2^3) + 1;
a(2) = 1^2 + 64*32^2 = 65537 is a prime factor of 2^(2^4) + 1;
a(3) = 127^2 + 64*194^2 = 2424833 is a prime factor of 2^(2^9) + 1;
a(4) = 2047^2 + 64*584^2 = 26017793 is a prime factor of 2^(2^12) + 1;
a(5) = 7295^2 + 64*406^2 = 63766529 is a prime factor of 2^(2^12) + 1;
- Allan Cunningham, Haupt-exponents of 2, The Quarterly Journal of Pure and Applied Mathematics, Vol. 37 (1906), pp. 122-145.
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isok(p) = if(p%8==1 && isprime(p), my(d=Mod(2, p)); d^((p-1)/4)==1 && d^2^valuation(p-1, 2)==1, return(0));
A283051
Positive integers n such that none of the primes of the form k*2^n + 1 (with k odd) divide any Fermat number F(m) = 2^(2^m) + 1, m >= 0.
Original entry on oeis.org
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