%N 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.
%C 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.
%e 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.
%e 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
%e For n = 13, the number can't be represented in this list as it would be 27A5 in base 13.
%Y See A087502 (which is the main entry for this sequence) for these numbers written in base 10. Cf. A023094, A159774.
%A Daniel Asimov (asimov(AT)msri.org), Mar 28 2009
%E a(5) corrected by William A. Hoffman III (whoff(AT)robill.com), Apr 19 2009
%E a(8) corrected by _Robert Tanniru_, Aug 09 2022
%E a(11)-a(12) from _Robert Tanniru_, Aug 11 2022, using A087502