A248018 Least number k > 0 such that n^k contains n*R_n in its decimal representation, or 0 if no such k exists.

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

Offset: 1

Author

Talha Ali, Sep 29 2014

Keywords

• base
• nonn
• hard
• more

Comments

R_n is the repunit of length n, i.e., R_n = (10^n-1)/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

Examples

			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.
		

Crossrefs

Cf. A002275.

Programs

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

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