

A270029


a(n) is the smallest b for which the baseb representation of n contains at least one 3 (or 0 if no such base exists).


11



0, 0, 4, 0, 0, 0, 4, 5, 6, 7, 4, 4, 4, 4, 4, 5, 5, 5, 4, 6, 6, 6, 4, 7, 7, 7, 4, 4, 4, 4, 4, 9, 5, 9, 4, 10, 10, 5, 4, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 17, 5, 5, 4, 5, 5, 7, 4, 7, 5, 7, 4, 4, 4, 4, 4, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 4, 4, 4, 4, 4, 5, 5, 5, 4, 26
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OFFSET

1,3


COMMENTS

a(n) > 0 for n >= 7 since 13 is n written in base n3.
The only perfect kth powers (k >= 2) that can appear in this sequence are 2^k and 3^k with k a prime number.


LINKS

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


MATHEMATICA

Table[SelectFirst[Range[4, 10^3], DigitCount[n, #, 3] > 0 &], {n, 7, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)


PROG

(PARI) a(n) = if ((n<7) && (n!=3), 0, my(b=4); while(!vecsearch(Set(digits(n, b)), 3), b++); b); \\ Michel Marcus, Mar 10 2016


CROSSREFS

Cf. A270027, A270028, A216194, A270030, A270031, A270032, A270033, A270034, A270035, A270039.
Sequence in context: A255263 A153011 A173532 * A028598 A272618 A265397
Adjacent sequences: A270026 A270027 A270028 * A270030 A270031 A270032


KEYWORD

nonn,base


AUTHOR

Nathan Fox, Mar 08 2016


STATUS

approved



