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COMMENTS
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Having sequences with limits (10^7) is not OEIS policy. We make an exception here. - T. D. Noe, Jul 11 2013
There are 3 other important informative parameters (A 4-dimensional sequence from an informative point of view) for each term of the sequence : (b,l,k) where b is the base powered, l is the number of primes added and k is the k-th prime where the sum of the consecutive primes begin : (2,2,2), (3,5,13), (2,2,18), (6,2,28), (23,47,32), (124,704,34), (19,25,46), (61,233,47), (5,11,55), (23,27,74), (1078,15442,74), (688,8116,78), (11,3,85), (2710,57856,87), (2,48,99), (14,320,100), (4120,105616,111), (89,345,135), (34,42,139), (35,45,140), (37,51,143), (909,12023,149), (43,65,168), (68,186,170), (28,20,174), (283,2137,205), (362,3102,206), (1171,17211,247), (22,6,273), (66,126,277), (173,907,292), (195,1107,303)
The limit (of 10^7) in the name/definition of the sequence is necessary because no power with exponent greater than 2 has been found for sums of primes beginning with first prime. Or beginning with many other primes. Naturally this limit could be much widened and alter the sequence; but this is why I put it in the name.
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