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A290177 Bases b for which there exists an integer y such that y^3 in base b consists of three identical digits. 4
18, 88916, 1147805, 6042955, 761357755, 1161183643 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A number b is a term if 1+b+b^2 can be multiplied by a number k < b to obtain a cube. The smallest candidate k can be easily obtained from the prime factorization of 1+b+b^2. For example, for b = 761357755 we have 1+b+b^2 = 3 * 7^2 * 2131 * 12277^3, so k = 3^2 * 7 * 2131^2, which happens to smaller than b.  a(7) > 10^10. - Giovanni Resta, Sep 02 2019

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..6.

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 = 7, and the base-b representation of y^3 is 111.

CROSSREFS

Cf. A290172, A290173, A290176, A290185.

Sequence in context: A051591 A146203 A192081 * A259364 A013762 A078352

Adjacent sequences:  A290174 A290175 A290176 * A290178 A290179 A290180

KEYWORD

nonn,base,more

AUTHOR

Jeffrey Shallit, Jul 23 2017

EXTENSIONS

a(5)-a(6) from Giovanni Resta, Sep 02 2019

STATUS

approved

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Last modified October 2 08:34 EDT 2022. Contains 357191 sequences. (Running on oeis4.)