Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #41 Jun 14 2021 11:53:22
%S 239,682,4443,12943,275807,6826318,26392464,30349818,54608393,
%T 54610269,103224943,275805068,419282318,1085592682,1268860318,
%U 1344783432,2321201748
%N Bases b for which there exists an integer y such that y^4 in base b looks like [c,d,c,d] for some base-b digits c, d.
%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 = 239, we have y = 78, and the base-b representation of y^4 is (2,170,2,170).
%t Select[Range[300000], Times @@ Table[ f[[1]]^(3 - Mod[f[[2]] - 1, 4]), {f, FactorInteger[1 + #^2]}] <= #^2 + 1 &] (* _Giovanni Resta_, Jul 26 2017 *)
%Y Cf. A290204.
%K base,nonn,more
%O 1,1
%A _Jeffrey Shallit_, Jul 25 2017
%E a(9)-a(17) from _Giovanni Resta_, Jul 26 2017