A290177 - OEIS

%I #18 Jun 14 2021 11:53:46

%S 18,88916,1147805,6042955,761357755,1161183643

%N Bases b for which there exists an integer y such that y^3 in base b consists of three identical digits.

%C A number b is a term if 1+b+b^2 can be multiplied by a number k < b to obtain a cube. The smallest candidate k can be easily obtained from the prime factorization of 1+b+b^2. For example, for b = 761357755 we have 1+b+b^2 = 3 * 7^2 * 2131 * 12277^3, so k = 3^2 * 7 * 2131^2, which happens to smaller than b.  a(7) > 10^10. - _Giovanni Resta_, Sep 02 2019

%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 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 = 18, we have y = 7, and the base-b representation of y^3 is 111.

%Y Cf. A290172, A290173, A290176, A290185.

%K nonn,base,more

%O 1,1

%A _Jeffrey Shallit_, Jul 23 2017

%E a(5)-a(6) from _Giovanni Resta_, Sep 02 2019