

A248018


Least number k > 0 such that n^k contains n*R_n in its decimal representation, or 0 if no such k exists.


0



1, 43, 119, 96, 186, 1740, 6177, 8421, 104191, 0, 946417
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OFFSET

1,2


COMMENTS

R_n is the repunit of length n, i.e., R_n = (10^n1)/9, A002275.
a(10^n) = 0 for all n > 0.  Derek Orr, Sep 29 2014
a(9) > 86000.  Derek Orr, Sep 29 2014
Note that a(2) = A030000(22), and a(3) = A063566(333), and that sequence is also related in a similar way to sequences from A063567 up to A063572.  Michel Marcus, Sep 30 2014


LINKS

Table of n, a(n) for n=1..11.


EXAMPLE

a(2) = 43 because 2^43 = 8796093022208 has the string '22' in it and 43 is the smallest power of 2 that produces such a result.
a(3) = 119 because 3^119 = 599003433304810403471059943169868346577158542512617035467 contains the string '333', and 119 is the smallest power of 3 that gives us such a result.


PROG

(Python)
def a(n):
..s = str(n)
..p = len(s)
..if s.count('1') == 1 and s.count('0') == p  1:
....return 0
..k = 1
..while not str(n**k).count(n*s):
....k += 1
..return k
n = 1
while n < 10:
..print(a(n), end=', ')
..n += 1
# Derek Orr, Sep 29 2014


CROSSREFS

Cf. A002275.
Sequence in context: A297412 A282294 A251075 * A262491 A029816 A044294
Adjacent sequences: A248015 A248016 A248017 * A248019 A248020 A248021


KEYWORD

base,nonn,hard,more


AUTHOR

Talha Ali, Sep 29 2014


EXTENSIONS

a(3) and a(5) corrected, a(6)a(8) added by Derek Orr, Sep 29 2014
a(4) corrected and a(9)a(11) added by Hiroaki Yamanouchi, Oct 01 2014


STATUS

approved



