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 base-b digits c, d.

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

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

References

Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit, The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations, Experimental Math, 28 (2019), 428-439.

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 Nagell-Ljunggren 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 base-b 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 A346278 A165495

Adjacent sequences: A290173 A290174 A290175 * A290177 A290178 A290179

Keyword

nonn,base

Author

Jeffrey Shallit, Jul 23 2017

Status

approved