A158877 Definition of a(n): in base-n arithmetic a(n) is the smallest positive integer that is doubled when its least significant digit is moved to become the most significant digit.

1012, 102, 13, 1031345242, 103524563142, 25, 10467842, 105263157894736842, 37, 10631694842

Offset

3,1

Comments

The problem has no solution in base 2, so sequence begins with the base-3 solution. The idea was suggested by a NY Times article (Sunday Magazine of Mar 29, 2009) -- in which Freeman Dyson is said to have solved the base-10 question almost instantaneously when it was posed to him -- and by the ensuing math-fun discussion.

Links

Table of n, a(n) for n=3..12.

Example

For n = 5, the smallest positive integer whose base-5 representation doubles when the rightmost digit is moved to become the leftmost digit is 8 = 13_5; 31_5 = 16.
For n = 8, the smallest positive integer whose base-8 representation doubles when the rightmost digit is moved to become the leftmost digit is 21 = 25_8; 52_8 = 42. - Robert Tanniru, Aug 09 2022
For n = 13, the number can't be represented in this list as it would be 27A5 in base 13.

Crossrefs

See A087502 (which is the main entry for this sequence) for these numbers written in base 10. Cf. A023094, A159774.

Sequence in context: A178349 A291962 A094946 * A159774 A072140 A080467

Adjacent sequences: A158874 A158875 A158876 * A158878 A158879 A158880

Keyword

nonn,base

Author

Daniel Asimov (asimov(AT)msri.org), Mar 28 2009

Extensions

a(5) corrected by William A. Hoffman III (whoff(AT)robill.com), Apr 19 2009

a(8) corrected by Robert Tanniru, Aug 09 2022

a(11)-a(12) from Robert Tanniru, Aug 11 2022, using A087502

Status

approved