A243304 Least number k > 0 such that 3^k contains at least an n-digit long substring of the infinite string "98765432109876543210987654...".

1, 5, 13, 50, 213, 536, 536, 536, 9354, 63202, 117150, 1314904, 2572181, 2572181

Offset

1,2

Comments

a(n+1) >= a(n) for all n.

Note that this sequence is "..at least an n-digit long substring...", not "..exactly an n-digit long substring...". Thus a(6) = a(7) = a(8) = 536. However, if it were "..exactly an n-digit long substring...", a(6) would be 810 and a(7) would be 1772. - Derek Orr, Sep 26 2014

a(15) > 10^7. If the definition were "exactly an n-digit long" then a(13) would be 4019359. - Delbert L. Johnson, Apr 13 2024

Links

Table of n, a(n) for n=1..14.

Example

3^5 = 243 contains a 2-digit substring of the infinite string "98765432109876543210987654..." (in this case, "43"). So a(2) = 5.

Prog

(Python)
def Rev(n):
  rev = ''
  for i in str(n):
    rev = i + rev
  return rev
def a(n):
  lst = []
  for b in range(1, 10**n):
    if len(str(3**b)) >= n:
      lst.append(b)
      break
  for k in range(lst[0], 50000):
    for i in range(10):
      s = ''
      s += str(i)
      for j in range(i+1, i+n):
        dig = j%10
        s+=str(dig)
      if str(3**k).find(Rev(s)) > -1:
        return k
n = 1
while n < 100:
  print(a(n), end=', ')
  n += 1

Crossrefs

Cf. A243295.

Sequence in context: A149537 A146689 A146657 * A238508 A151274 A149538

Adjacent sequences: A243301 A243302 A243303 * A243305 A243306 A243307

Keyword

nonn,base,more,hard,less

Author

Derek Orr, Jun 04 2014

Extensions

a(10)-a(12) from Hiroaki Yamanouchi, Sep 26 2014

a(13)-a(14) from Delbert L. Johnson, Apr 13 2024

Status

approved