A290176 - OEIS

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.

%I #18 Jun 14 2021 10:02:01

%S 7,38,41,57,68,117,239,268,515,682,882,1068,1393,1744,1958,1985,2072,

%T 2928,2943,3141,4005,4030,4443,5357,5604,5818,6072,6948,8119,8827,

%U 9210,9466,10133,11018,11389,12238,12943,13545,13807,14256,14557,15618,16432,17684,19703,23156,23382,27493,27590,29718,30235

%N 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.

%C 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

%D 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.

%H Robert Israel, <a href="/A290176/b290176.txt">Table of n, a(n) for n = 1..512</a>

%H Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit, <a href="https://arxiv.org/abs/1707.03894">The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations</a>, preprint, arXiv:1707.03894 [math.NT], July 14 2017.

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

%Y Cf. A290172, A290173, A290177, A290185.

%Y Contains all members of A002315 except 1.

%K nonn,base

%O 1,1

%A _Jeffrey Shallit_, Jul 23 2017