

A290176


Bases b for which there exists an integer y such that y^3 in base b looks like [c,d,c,d] for some baseb digits c, d.


5



7, 38, 41, 57, 68, 117, 239, 268, 515, 682, 882, 1068, 1393, 1744, 1958, 1985, 2072, 2928, 2943, 3141, 4005, 4030, 4443, 5357, 5604, 5818, 6072, 6948, 8119, 8827, 9210, 9466, 10133, 11018, 11389, 12238, 12943, 13545, 13807, 14256, 14557, 15618, 16432, 17684, 19703, 23156, 23382, 27493, 27590, 29718, 30235
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OFFSET

1,1


COMMENTS

Numbers b such that there exists x such that x*(b^2+1) is a cube and 1 <= x < b^2.  Robert Israel, Oct 05 2020


LINKS

Robert Israel, Table of n, a(n) for n = 1..512
Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit, The Generalized NagellLjunggren Problem: Powers with Repetitive Representations, preprint, arXiv:1707.03894 [math.NT], July 14 2017.


EXAMPLE

For example, for b = 7, we have y = 10, and the baseb representation of y^3 is 2626.


CROSSREFS

Cf. A290172, A290173, A290177, A290185.
Contains all members of A002315 except 1.
Sequence in context: A127729 A129736 A220852 * A003352 A165495 A034858
Adjacent sequences: A290173 A290174 A290175 * A290177 A290178 A290179


KEYWORD

nonn,base


AUTHOR

Jeffrey Shallit, Jul 23 2017


STATUS

approved



