Prime numbers that are the sum of consecutive 6-th powers.
4889, 66377, 977611, 1977611, 18645331, 71396911, 101659963, 271739011, 1091341291, 1761506059, 2208293491, 5559852377, 6121341211, 6746908739, 9834492799, 14831963339, 18751258931, 21303493691, 32484102689, 42065402653, 59854576963, 101228136259
1
These primes are the sum of 3, 6, 7, 14, 21, or 42 consecutive 6-th powers. See S000785.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
(Mma) ss = {3, 6, 7, 14, 21, 42}; nn = 400; sq = Table[n^6, {n, nn}]; t6 = Table[Select[Plus @@@ Partition[sq, n, 1], PrimeQ], {n, ss}]; mx = Min[Select[Max /@ t6, # > 0 &]]; Select[Union[Flatten[t6]], # <= mx &]
Cf. A163251, A165347, S000785, S000787-S000789.
nonn
T. D. Noe, Dec 08 2015