A289390 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.

239, 682, 4443, 12943, 275807, 6826318, 26392464, 30349818, 54608393, 54610269, 103224943, 275805068, 419282318, 1085592682, 1268860318, 1344783432, 2321201748

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

Table of n, a(n) for n=1..17.

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 = 239, we have y = 78, and the base-b representation of y^4 is (2,170,2,170).

Mathematica

Select[Range[300000], Times @@ Table[ f[[1]]^(3 - Mod[f[[2]] - 1, 4]), {f, FactorInteger[1 + #^2]}] <= #^2 + 1 &] (* Giovanni Resta, Jul 26 2017 *)

Crossrefs

Cf. A290204.

Sequence in context: A142557 A164290 A201787 * A118574 A142854 A065098

Adjacent sequences: A289387 A289388 A289389 * A289391 A289392 A289393

Keyword

base,nonn,more

Author

Jeffrey Shallit, Jul 25 2017

Extensions

a(9)-a(17) from Giovanni Resta, Jul 26 2017

Status

approved