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%I #24 Nov 14 2014 14:36:52
%S 1,3,5,7,10,11,12,13,15,17,19,20,21,25,26,27,28,29,30,31,34,35,37,39,
%T 40,41,43,45,48,49,50,51,52,53,55,57,58,60,61,63,65,67,68,70,73,74,75,
%U 76,78,79,80,82,84,85,87,89,90,91,93,95,97,100,101,102,103
%N Integers generated by (a^k+b^k)/(a+b) for all possible positive integer values of a,b,k with b>a.
%C This form, (a^k+b^k)/(a+b), is a generalization of the Fermat numbers.
%C Not all integers are in this set.
%C See A227979 for the complement of this sequence.
%H Robert Price, <a href="/A229791/b229791.txt">Table of n, a(n) for n = 1..134</a>
%H J. Brillhart et al., <a href="http://dx.doi.org/10.1090/conm/022">Factorizations of b^n +- 1</a>, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
%H H. Dubner and T. Granlund, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/DUBNER/dubner.html">Primes of the Form (b^n+1)/(b+1)</a>, J. Integer Sequences, 3 (2000), #P00.2.7.
%H H. Lifchitz, <a href="http://www.primenumbers.net/Henri/us/MersFermus.htm">Mersenne and Fermat primes field</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>.
%t limit=105; lst = {}; Do[p = (a^k + b^k)/(a + b); If[p <= limit && IntegerQ[p], AppendTo[lst, p]], {k, Log[2,3*limit+1]}, {b, 2, limit*2}, {a, b-1}]; Union[lst]
%Y A few of the sequences using this form that identify primes are A000978, A007658, A057469, A128066, A057171, A082387, A122853, A128335.
%K nonn
%O 1,2
%A _Robert Price_, Sep 29 2013