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%I #2 Mar 30 2012 18:40:50
%S 17,114,371,708,1589,5286,15943,32504,81801,147338,214315,303356,
%T 452413,1300014,2288431,3434528,5406625,7476866,9999123,12836084,
%U 16389861,20349158,24747735,30133496,37300393,48373610,66027291,98557468
%N Partial sums of A078902.
%C It is unknown if this is a finite or infinite sequence. Can it ever have a prime value after a(1) = 17? It can be semiprime, as 371 = 7 * 53; 1589 = 7 * 227; 15943 = 107 * 149; 214315 = 5 * 42863; 2288431 = 23 * 99497; and 16389861 = 3 * 5463287.
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/GeneralizedFermatNumber.html">Generalized Fermat Number.</a>
%F SUM[i=1..n] {primes of the form (k+1)^2^m + k^2^m, with m>1.}
%e a(29) = 17 + 97 + 257 + 337 + 881 + 3697 + 10657 + 16561 + 49297 + 65537 + 66977 + 89041 + 149057 + 847601 + 988417 + 1146097 + 1972097 + 2070241 + 2522257 + 2836961 + 3553777 + 3959297 + 4398577 + 5385761 + 7166897 + 11073217 + 17653681 + 32530177 + 41532497 + 44048497.
%Y Cf. A000040, A001358, A019434, A077659, A078900, A078901, A078902, A080131, A080208.
%K nonn
%O 1,1
%A _Jonathan Vos Post_, Feb 06 2010
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