A172521 Partial sums of A078902.

17, 114, 371, 708, 1589, 5286, 15943, 32504, 81801, 147338, 214315, 303356, 452413, 1300014, 2288431, 3434528, 5406625, 7476866, 9999123, 12836084, 16389861, 20349158, 24747735, 30133496, 37300393, 48373610, 66027291, 98557468

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..28.

Eric W. Weisstein, Generalized Fermat Number.

Formula

SUM[i=1..n] {primes of the form (k+1)^2^m + k^2^m, with m>1.}

Example

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.

Crossrefs

Cf. A000040, A001358, A019434, A077659, A078900, A078901, A078902, A080131, A080208.

Sequence in context: A197360 A367940 A289472 * A349879 A226688 A070144

Adjacent sequences: A172518 A172519 A172520 * A172522 A172523 A172524

Keyword

nonn

Author

Jonathan Vos Post, Feb 06 2010

Status

approved