

A290177


Bases b for which there exists an integer y such that y^3 in base b consists of three identical digits.


4




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 NagellLjunggren Problem: Powers with Repetitive Representations, Experimental Math, 28 (2019), 428439.


LINKS

Table of n, a(n) for n=1..6.
Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit, The Generalized NagellLjunggren 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 baseb 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



