

A270030


a(n) is the smallest b for which the baseb representation of n contains at least one 4 (or 0 if no such base exists).


11



0, 0, 0, 5, 0, 0, 0, 0, 5, 6, 7, 8, 9, 5, 11, 6, 13, 7, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 7, 7, 7, 7, 5, 8, 8, 8, 8, 5, 6, 9, 9, 9, 5, 5, 5, 5, 5, 5, 11, 11, 6, 7, 5, 12, 12, 12, 6, 5, 6, 6, 6, 6, 5, 6, 14, 7, 8, 5, 5, 5, 5, 5, 5, 16, 6, 7, 7, 5, 7, 7, 6, 7, 5, 9, 18, 18, 6, 5, 19
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OFFSET

1,4


COMMENTS

a(n) > 0 for n >= 9 since 14 is n written in base n4.
The only perfect kth powers (k >= 2) that can appear in this sequence are 2^k, 3^k, or 4^k, with k a prime number.


LINKS



MATHEMATICA

Table[SelectFirst[Range[5, 10^3], DigitCount[n, #, 4] > 0 &], {n, 9, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)


PROG

(PARI) a(n) = if ((n<9) && (n!=4), 0, my(b=5); while(!vecsearch(Set(digits(n, b)), 4), b++); b); \\ Michel Marcus, Mar 10 2016


CROSSREFS

Cf. A268236, A268237, A270027, A270028, A216194, A270029, A270031, A270032, A270033, A270034, A270035, A270040.


KEYWORD

nonn,base


AUTHOR



STATUS

approved



