A270035 a(n) is the smallest b for which the base-b representation of n contains at least one 9 (or 0 if no such base exists).

0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 10, 21, 11, 23, 12, 25, 13, 27, 14, 29, 10, 31, 16, 11, 17, 35, 12, 37, 19, 13, 10, 41, 14, 43, 11, 15, 23, 47, 12, 49, 10, 17, 13, 53, 18, 11, 14, 19, 29, 59, 10, 61, 31, 21, 16, 13, 11, 67, 17, 23, 10, 71

Offset

1,9

Comments

a(n) > 0 for n >= 19 since 19 is n written in base n-9.

The only perfect k-th powers (k >= 2) that can appear in this sequence are m^k with 2 <= m <= 9 and k a prime number.

Links

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

Mathematica

Table[SelectFirst[Range[10, 1200], DigitCount[n, #, 9] > 0 &], {n, 19, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)

Prog

(PARI) a(n) = if ((n<19) && (n!=9), 0, my(b=10); while(!vecsearch(Set(digits(n, b)), 9), b++); b); \\ Michel Marcus, Mar 10 2016

Crossrefs

Cf. A270027, A270028, A216194, A270029, A270030, A270031, A270032, A270033, A270034, A270045.

Sequence in context: A058472 A058474 A285476 * A228636 A306758 A340983

Adjacent sequences: A270032 A270033 A270034 * A270036 A270037 A270038

Keyword

nonn,base

Author

Nathan Fox, Mar 08 2016

Status

approved