A063567 -id:A063567 - cp's OEIS frontend

A062521 4^a(n) is smallest nonnegative power of 4 containing the string 'n'.

5, 0, 4, 7, 1, 4, 2, 10, 7, 6, 5, 20, 25, 35, 9, 29, 2, 17, 15, 11, 28, 9, 36, 29, 5, 4, 9, 19, 24, 16, 11, 37, 38, 43, 35, 14, 8, 15, 7, 21, 6, 11, 16, 11, 9, 14, 21, 18, 10, 16, 26, 20, 30, 8, 14, 8, 4, 10, 25, 22, 22, 29, 9, 7, 3, 8, 23, 12, 14, 17, 23, 13, 12, 15, 15, 22

Offset: 0

Robert G. Wilson v, Jun 24 2001

Cf. A030000. Essentially the same as A063567.

Table[k = 0; While[ StringPosition[ ToString[4^k], ToString[n] ] == {}, k++ ]; k, {n, 0, 75} ]

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

Original entry on oeis.org

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

Offset: 1

Talha Ali, Sep 29 2014

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

			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.

Cf. A002275.

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

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

cp's OEIS Frontend

A062521 4^a(n) is smallest nonnegative power of 4 containing the string 'n'.

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

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