A290172 Bases b for which there exists an integer y such that y^2 in base b consists of three identical digits.

18, 22, 30, 68, 146, 292, 313, 423, 439, 499, 521, 581, 653, 699, 710, 787, 1047, 1353, 1425, 1660, 1714, 2060, 2174, 2198, 2272, 2819, 3019, 3130, 3445, 3789, 4366, 4526, 4611, 4620, 4624, 4701, 4788, 4972, 5261, 5421, 5656, 6057, 6106, 6158, 6205, 6895, 6927, 7163, 7527, 7627, 7733, 9317, 9353, 10761, 11092

Offset

1,1

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

Giovanni Resta, Table of n, a(n) for n = 1..10000

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 = 18, we have y = 49, and the base-b representation of y^2 is 777.

Mathematica

r[b_] := Reduce[0 < x < b && y > 0 && y^2 == x + b x + b^2 x, {x, y}, Integers]; Reap[For[b = 2, b < 12000, b++, If[r[b] =!= False, Print[b]; Sow[b]]]][[2, 1]] (* Jean-François Alcover, Jul 23 2017 *)

Crossrefs

Cf. A290173, A290176, A290177, A290185.

Sequence in context: A049734 A096282 A250737 * A031407 A267826 A339473

Adjacent sequences: A290169 A290170 A290171 * A290173 A290174 A290175

Keyword

nonn,base

Author

Jeffrey Shallit, Jul 23 2017

Status

approved