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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.
0
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
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
KEYWORD
base,nonn,more
AUTHOR
Jeffrey Shallit, Jul 25 2017
EXTENSIONS
a(9)-a(17) from Giovanni Resta, Jul 26 2017
STATUS
approved