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%I #9 Aug 12 2015 05:27:17
%S 2,3,135812051,1223891771,1287820181,2441406251,13062296531,
%T 96890604731,2541865828331,10000068703187,34535772846139,
%U 34620821857463,69142313298269,106993206981587,106994426090389,107007486776213
%N Primes p = k^13 + m^13 + n^13 with nonnegative integer bases k, m, n.
%C Necessarily (I) two bases are even and one is odd or (II) all bases are odd.
%C 2 = 1^13 + 1^13 is the only 2-item term of sequence because with an odd exponent e a^e + b^e has the divisor a+b.
%C List of (k,m,n): (0,1,1) (1,1,1) (3,4,4) (3,3,5) (2,4,5) (1,5,5) (2,3,6) (1,3,7) (1,1,9) (3,4,10) (2,6,11) (5,7,11) (7,11,11) (2,3,12) (2,5,12) (5,6,12) (4,6,13) (8,8,13) (4,12,13) (4,11,14) (6,11,14) (5,12,14) (11,12,14) (3,14,14) (2,2,15) (1,3,15) (2,6,15) (14,14,15) (7,15,15) (1,6,16) (2,13,16) (2,4,17) (3,9,17) (5,9,17) (1,11,17) (2,12,17) (6,14,17) (11,12,18) (10,13,18) (14,15,18) (11,18,18) (1,3,19) (4,8,19) (3,9,19) (7,11,19) (14,14,19) (3,15,19) (7,15,19) (12,15,20) (11,16,20)
%e 3^13 + 3^13 + 4^13 = 135812051 = prime(7688710), 3rd term.
%e 3^13 + 3^13 + 5^13 = 1223891771 = prime(61596945), 4th term, smallest with 3 prime bases.
%e 5^13 + 7^13 + 11^13 = 34620821857463, 12th term, the smallest with 3 different prime bases.
%Y Cf. A000040, A001022.
%K nonn
%O 1,1
%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 22 2010
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