Prime numbers that are the sum of consecutive 12-th powers.
84998999651, 93397675335971, 1087241227167013, 28541073656868611, 28764217670095207, 242219385297406711, 891161285028753379, 9374114995098123379, 15622297824266188673, 28973523463966221251, 58919959903331196133, 67370953870277641939, 113122707759226151039
1
These primes are the sum of 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365, or 2730 consecutive 12-th powers. See S000785.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
(Mma) ss = {3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365, 2730}; nn = 400; sq = Table[n^12, {n, nn}]; t12 = Table[Select[Plus @@@ Partition[sq, n, 1], PrimeQ], {n, ss}]; mx = Min[Select[Max /@ t12, # > 0 &]]; Select[Union[Flatten[t12]], # <= mx &]
Cf. A163251, A165347, S000785-S000788.
nonn
T. D. Noe, Dec 08 2015