A270032 a(n) is the smallest b for which the base-b representation of n contains at least one 6 (or 0 if no such base exists).

0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 7, 8, 9, 10, 11, 12, 13, 7, 15, 8, 17, 9, 19, 10, 7, 11, 23, 8, 25, 13, 9, 7, 29, 10, 31, 8, 11, 17, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 9, 9, 9, 9, 9, 9, 7, 10, 10, 10, 10, 10, 10, 7, 8, 11, 11, 11, 11, 11, 7, 12, 8, 12, 12, 12

Offset

1,6

Comments

a(n) > 0 for n >= 13 since 16 is n written in base n-6.

The only perfect k-th powers (k >= 2) that can appear in this sequence are m^k with 2 <= m <= 6 and k a prime number.

Links

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

Mathematica

Table[SelectFirst[Range[7, 1200], DigitCount[n, #, 6] > 0 &], {n, 13, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)

Prog

(PARI) a(n) = if ((n<13) && (n!=6), 0, my(b=7); while(!vecsearch(Set(digits(n, b)), 6), b++); b); \\ Michel Marcus, Mar 10 2016

Crossrefs

Cf. A270027, A270028, A216194, A270029, A270030, A270031, A270033, A270034, A270035, A270042.

Sequence in context: A079683 A115528 A354995 * A340980 A305671 A228633

Adjacent sequences: A270029 A270030 A270031 * A270033 A270034 A270035

Keyword

nonn,base

Author

Nathan Fox, Mar 08 2016

Status

approved