

A290173


Bases b for which there exists an integer y such that y^2 in base b looks like [c,d,c,d,c,d] for some baseb digits c, d.


4



68, 313, 699, 4366, 51567, 234924, 686287, 3526450, 3652434, 301121223, 1250094151, 3072665429, 4507947478
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OFFSET

1,1


COMMENTS



REFERENCES

Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit, The Generalized NagellLjunggren Problem: Powers with Repetitive Representations, Experimental Math, 28 (2019), 428439.


LINKS



EXAMPLE

For example, for b = 68, we have y = 160797, and the baseb representation of y^2 is (17,53,17,53,17,53).


MATHEMATICA

core[n_] := Block[{f = Transpose@ FactorInteger@ n}, Times @@ (f[[1]]^ Mod[f[[2]], 2])]; Select[Range[3*10^5], core[1 + # + #^2] core[1  # + #^2] < #^2 &] (* Giovanni Resta, Jul 27 2017 *)


PROG

(PARI) isok(k) = core(1+k^2+k^4) < k^2; \\ Michel Marcus, Jul 28 2017


CROSSREFS



KEYWORD

nonn,base,more


AUTHOR



EXTENSIONS



STATUS

approved



