

A270033


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


11



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
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OFFSET

1,7


COMMENTS

a(n) > 0 for n >= 15 since 17 is n written in base n7.
The only perfect kth 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: A067485 A180225 A127886 * A085121 A228634 A229659
Adjacent sequences: A270030 A270031 A270032 * A270034 A270035 A270036


KEYWORD

nonn,base


AUTHOR

Nathan Fox, Mar 08 2016


STATUS

approved



