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%I #21 Mar 27 2022 22:53:58
%S 274177,319489,6700417,825753601,1214251009,6487031809,646730219521,
%T 6597069766657,25409026523137,31065037602817,46179488366593,
%U 151413703311361,231292694251438081,1529992420282859521,2170072644496392193,3603109844542291969
%N Primes congruent to 1 (mod 3) that divide some Fermat number.
%C Subsequence of A014752.
%D Allan Cunningham, Haupt-exponents of 2, The Quarterly Journal of Pure and Applied Mathematics, Vol. 37 (1906), pp. 122-145.
%H Wilfrid Keller, <a href="http://www.prothsearch.com/fermat.html">Prime factors k.2^n + 1 of Fermat numbers F_m</a>.
%F A002476 INTERSECT A023394.
%e a(1) = 503^2 + 27*28^2 = 274177 is a prime factor of 2^(2^6) + 1;
%e a(2) = 383^2 + 27*80^2 = 319489 is a prime factor of 2^(2^11) + 1;
%e a(3) = 887^2 + 27*468^2 = 6700417 is a prime factor of 2^(2^5) + 1;
%e a(4) = 27017^2 + 27*1884^2 = 825753601 is a prime factor of 2^(2^16) + 1;
%e a(5) = 2561^2 + 27*6688^2 = 1214251009 is a prime factor of 2^(2^15) + 1;
%o (PARI) isok(p) = if(p%6==1 && isprime(p), my(z=znorder(Mod(2, p))); z>>valuation(z, 2)==1, return(0));
%Y Cf. A002476, A014752, A023394, A204620, A229850, A229853.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Feb 07 2022