A111103 -id:A111103

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A111131

Least cube greater than its predecessor such that their difference is a prime or a prime multiplied by a power of two.

+10
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

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OFFSET

1,2

COMMENTS

The sequence was conceived as n^3 is the sum of n primes as shown below:

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

Table of n, a(n) for n=1..37.

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.

KEYWORD

nonn

AUTHOR

Giovanni Teofilatto, Oct 14 2005

EXTENSIONS

Edited and extended by Robert G. Wilson v, Oct 18 2005

Name clarified by Peter Munn, Jun 17 2021

STATUS

approved

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