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Group successively larger prime numbers so that the sum of the n-th group is a multiple of n. Sequence gives the sum for each group.
4

%I #3 Dec 05 2013 19:55:33

%S 2,8,18,72,60,78,553,1336,4743,4370,726,1524,14027,2380,6330,24800,

%T 9214,5886,19038,2240,25515,5192,46138,9456,42125,10842,56619,103068,

%U 170868,85140,55149,88800,7062,42908,199360,24444,87949,301188,1110057

%N Group successively larger prime numbers so that the sum of the n-th group is a multiple of n. Sequence gives the sum for each group.

%t NextPrime[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; a = {}; k = 1; Do[s = 0; While[k = NextPrime[k]; s = s + k; !IntegerQ[s/n], ]; a = Append[a, s], {n, 1, 40}]; a

%Y Cf. A000040, A074129, A074130, A074131.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Aug 27 2002

%E (2), (3, 5), (7, 11), (13, 17, 19, 23), (29, 31), (37, 41), (43, 47, 53, 59, 61, 67, 71, 73, 79), (83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139), (149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, ..., 269), ...

%E Edited, corrected and extended by _Robert G. Wilson v_, Aug 29 2002