cp's OEIS Frontend

A059711 Smallest base in which n is a repdigit.

%I A059711 #12 Apr 07 2018 03:56:46
%S A059711 2,2,3,2,3,4,5,2,3,8,4,10,5,3,6,2,7,16,5,18,9,4,10,22,5,24,3,8,6,28,9,
%T A059711 2,7,10,16,6,8,36,18,12,3,40,4,6,10,8,22,46,7,48,9,16,12,52,8,10,13,7,
%U A059711 28,58,9,60,5,2,15,12,10,66,16,22,9,70,11,8,36,14,18,10,12,78,3,26,40,82,11,4
%N A059711 Smallest base in which n is a repdigit.
%C A059711 Numbers n such that a(n) < n - 1 correspond to Brazilian numbers (A125134); conversely, positive numbers n such that a(n) >= n - 1 correspond to A220570. - _Rémy Sigrist_, Apr 04 2018
%H A059711 Rémy Sigrist, <a href="/A059711/b059711.txt">Table of n, a(n) for n = 0..10000</a>
%F A059711 From _Rémy Sigrist_, Apr 04 2018: (Start)
%F A059711 a(n) <= n - 1 for any n >= 3.
%F A059711 a(2^n-1) = 2 for any n >= 0.
%F A059711 a(A048328(n)) <= 3 for any n >= 0.
%F A059711 a(A048329(n)) <= 4 for any n >= 0.
%F A059711 a(A048330(n)) <= 5 for any n >= 0.
%F A059711 a(A048331(n)) <= 6 for any n >= 0.
%F A059711 a(A048332(n)) <= 7 for any n >= 0.
%F A059711 a(A048333(n)) <= 8 for any n >= 0.
%F A059711 a(A048334(n)) <= 9 for any n >= 0.
%F A059711 a(A010785(n)) <= 10 for any n >= 0.
%F A059711 a(A048335(n)) <= 11 for any n >= 0.
%F A059711 a(A048336(n)) <= 12 for any n >= 0.
%F A059711 a(A048337(n)) <= 13 for any n >= 0.
%F A059711 a(A048338(n)) <= 14 for any n >= 0.
%F A059711 a(A048339(n)) <= 15 for any n >= 0.
%F A059711 a(A048340(n)) <= 16 for any n >= 0.
%F A059711 (End)
%e A059711 a(13) = 3 since 13 in base 3 is 111.
%o A059711 (PARI) a(n) = for (b=2, oo, if (#Set(digits(n, b))<=1, return (b))) \\ _Rémy Sigrist_, Apr 04 2018
%Y A059711 Cf. A010785, A125134, A048328, A048329, A048330, A048331, A048332, A048333, A048334, A048335, A048336, A048337, A048338, A048339, A048340, A220570.
%K A059711 base,easy,nonn
%O A059711 0,1
%A A059711 _Erich Friedman_, Feb 19 2001
%E A059711 Example clarified by _Harvey P. Dale_, Oct 11 2015
%E A059711 Terms a(0) = 2, a(1) = 2 and a(2) = 3 prepended by _Rémy Sigrist_, Apr 04 2018