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

3,1

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

Links

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

Example

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.)

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;

Crossrefs

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

Sequence in context: A364904 A140387 A023094 * A070628 A147514 A291155

Adjacent sequences: A087499 A087500 A087501 * A087503 A087504 A087505

Keyword

nonn,base

Author

Pontus von Brömssen, Sep 10 2003

Status

approved