A270033 a(n) is the smallest b for which the base-b representation of n contains at least one 7 (or 0 if no such base exists).

0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 9, 10, 11, 12, 13, 14, 15, 8, 17, 9, 19, 10, 21, 11, 23, 8, 25, 13, 9, 14, 29, 10, 31, 8, 11, 17, 35, 9, 37, 19, 13, 8, 41, 14, 43, 11, 9, 23, 47, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 8, 10, 10, 10, 10, 10, 10, 10, 8, 11, 11

Offset

1,7

Comments

a(n) > 0 for n >= 15 since 17 is n written in base n-7.

The only perfect k-th powers (k >= 2) that can appear in this sequence are m^k with 2 <= m <= 7 and k a prime number.

Links

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

Mathematica

Table[SelectFirst[Range[8, 1200], DigitCount[n, #, 7] > 0 &], {n, 15, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)

Prog

(PARI) a(n) = if ((n<15) && (n!=7), 0, my(b=8); while(!vecsearch(Set(digits(n, b)), 7), b++); b); \\ Michel Marcus, Mar 10 2016

Crossrefs

Cf. A270027, A270028, A216194, A270029, A270030, A270031, A270032, A270034, A270035, A270043.

Sequence in context: A180225 A353294 A127886 * A085121 A228634 A229659

Adjacent sequences: A270030 A270031 A270032 * A270034 A270035 A270036

Keyword

nonn,base

Author

Nathan Fox, Mar 08 2016

Status

approved