A270030 a(n) is the smallest b for which the base-b representation of n contains at least one 4 (or 0 if no such base exists).

0, 0, 0, 5, 0, 0, 0, 0, 5, 6, 7, 8, 9, 5, 11, 6, 13, 7, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 7, 7, 7, 7, 5, 8, 8, 8, 8, 5, 6, 9, 9, 9, 5, 5, 5, 5, 5, 5, 11, 11, 6, 7, 5, 12, 12, 12, 6, 5, 6, 6, 6, 6, 5, 6, 14, 7, 8, 5, 5, 5, 5, 5, 5, 16, 6, 7, 7, 5, 7, 7, 6, 7, 5, 9, 18, 18, 6, 5, 19

Offset

1,4

Comments

a(n) > 0 for n >= 9 since 14 is n written in base n-4.

The only perfect k-th powers (k >= 2) that can appear in this sequence are 2^k, 3^k, or 4^k, with k a prime number.

Links

Nathan Fox, Table of n, a(n) for n = 1..10000

Mathematica

Table[SelectFirst[Range[5, 10^3], DigitCount[n, #, 4] > 0 &], {n, 9, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)

Prog

(PARI) a(n) = if ((n<9) && (n!=4), 0, my(b=5); while(!vecsearch(Set(digits(n, b)), 4), b++); b); \\ Michel Marcus, Mar 10 2016

Crossrefs

Cf. A268236, A268237, A270027, A270028, A216194, A270029, A270031, A270032, A270033, A270034, A270035, A270040.

Sequence in context: A324323 A005078 A284446 * A284104 A369732 A260911

Adjacent sequences: A270027 A270028 A270029 * A270031 A270032 A270033

Keyword

nonn,base

Author

Nathan Fox, Mar 08 2016

Status

approved