1,2

a(9)-a(11) = {1, 4, 14}. a(13) = 78. a(16) = 8. a(18)-a(19) = {11, 26}. a(22) = 5. a(n) is greater than 100 for n = {7, 8, 12, 14, 15, 17, 20, 21, 23, ...}. Smallest primes p such that p^n equal to the sum of 3 consecutive primes are listed in A122706(n) = {23, 7, 11, 29, 79, 29, 509, 53, 467, 1571, 61, 7, 1553, 31, 1097, 11, 397, 11, 163, 677, 23, ...}.

a(1) = 0 because there is no power of 2 that is a sum of 3 consecutive primes.

Prime(5)^2=11^2=121 can be written as 37+41+43, therefore a(n=5)=2.

Cf. A122706.

Adjacent sequences: A123991 A123992 A123993 this_sequence A123995 A123996 A123997

Sequence in context: A066539 A095390 A033384 this_sequence A135124 A070931 A095533

hard,more,nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 31 2006, Nov 02 2006

Corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 13 2007