cp's OEIS Frontend

A270031 a(n) is the smallest b for which the base-b representation of n contains at least one 5 (or 0 if no such base exists).

%I A270031 #23 Jun 29 2019 01:39:37
%S A270031 0,0,0,0,6,0,0,0,0,0,6,7,8,9,10,11,6,13,7,15,8,17,6,19,10,7,11,23,6,6,
%T A270031 6,6,6,6,6,7,7,7,7,7,6,8,8,8,8,8,6,9,9,9,9,9,6,7,10,10,10,10,6,11,7,
%U A270031 11,11,11,6,6,6,6,6,6,6,13,13,13,7,13,6,14,14,14,14,7,6,7,7,7,7,7
%N A270031 a(n) is the smallest b for which the base-b representation of n contains at least one 5 (or 0 if no such base exists).
%C A270031 a(n) > 0 for n >= 11 since 15 is n written in base n-5.
%C A270031 The only perfect k-th powers (k >= 2) that can appear in this sequence are m^k with 2 <= m <= 5 and k a prime number.
%H A270031 Nathan Fox, <a href="/A270031/b270031.txt">Table of n, a(n) for n = 1..10000</a>
%t A270031 Table[SelectFirst[Range[6, 10^3], DigitCount[n, #, 5] > 0 &], {n, 11, 120}] (* _Michael De Vlieger_, Mar 10 2016, Version 10 *)
%o A270031 (PARI) a(n) = if ((n<11) && (n!=5), 0, my(b=6); while(!vecsearch(Set(digits(n, b)), 5), b++); b); \\ _Michel Marcus_, Mar 10 2016
%Y A270031 Cf. A270027, A270028, A216194, A270029, A270030, A270032, A270033, A270034, A270035, A270041.
%K A270031 nonn,base
%O A270031 1,5
%A A270031 _Nathan Fox_, Mar 08 2016