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 A111131 Least cube greater than its predecessor such that their difference is a prime or a power of two times a prime. 1
 1, 8, 27, 64, 125, 343, 729, 1000, 1331, 1728, 2744, 3375, 4913, 5832, 8000, 10648, 13824, 15625, 17576, 21952, 24389, 35937, 42875, 50653, 54872, 59319, 68921, 74088, 79507, 103823, 132651, 166375, 175616, 195112, 205379, 300763, 314432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sequence was conceived as n^3 is the sum of n primes as shown in the example line. 8=1+7, 27=8+19, 64=27+37, 125=64+61, 343=125+2*109, 729=343+2*193, 1000=729+271, .... Cube roots are 1,2,3,4,5,7,9,10,11,12,14,15,17,18,20,22,24,25,26,... LINKS MATHEMATICA a[1] = 1; a[n_] := a[n] = Block[{c = a[n - 1], j}, k = c^(1/3) + 1; While[j = 1; While[ IntegerQ[(k^3 - c)/j], j *= 2]; ! PrimeQ[2(k^3 - c)/j], k++ ]; k^3]; Table[ a[n], {n, 37}] (* Robert G. Wilson v *) CROSSREFS See A111103 for another version. Sequence in context: A052064 A125496 A030289 * A111103 A076969 A179163 Adjacent sequences:  A111128 A111129 A111130 * A111132 A111133 A111134 KEYWORD nonn AUTHOR Giovanni Teofilatto, Oct 14 2005 EXTENSIONS Edited and extended by Robert G. Wilson v, Oct 18 2005 STATUS approved

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Last modified August 3 19:49 EDT 2020. Contains 336201 sequences. (Running on oeis4.)