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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
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
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
KEYWORD
nonn,base,more
AUTHOR
Jeffrey Shallit, Jul 23 2017
EXTENSIONS
a(5)-a(6) from Giovanni Resta, Sep 02 2019
STATUS
approved