A087502 Smallest positive integer which when written in base n is doubled when the last digit is put first.

32, 18, 8, 10993850, 2129428800, 21, 5064320, 105263157894736842, 40, 64609423538, 5712, 65, 58774271029236501660840264682112, 67650, 96, 833, 586081355679130611935159482937228562988190880, 133

Offset: 3

Author

Pontus von Brömssen, Sep 10 2003

Keywords

• nonn
• base

Comments

a(n) is the smallest integer of the form x*(n^d-1)/(2n-1) for integer x and d, where 1 < x < n and d > 1. x is the last digit and d is the number of digits of a(n) in base n. - Pontus von Brömssen, Jan 06 2019

Examples

			a(10) = 105263157894736842 because 2*105263157894736842 = 210526315789473684 and no smaller number has this property. (Leading zeros are not allowed, otherwise 2*052631578947368421 = 105263157894736842 would be a smaller solution.)
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 3..221

Crossrefs

See A158877 for these numbers written in base n. Cf. A023094, A034089, A081463, A087502.

Programs

Maple

A087502 := proc(n) local d,a; d := 1; a := n; while a>=n do d := d+1; a := denom((2^d-1)/(2*n-1)); od; return(max(2,a)*(n^d-1)/(2*n-1)); end proc;