A243295 Least number k > 0 such that 3^k contains an n-digit long substring of the infinite string "0123456789012345678901234567890123456...".

1, 8, 15, 57, 102, 332, 2345, 2345, 10110, 118745, 127188, 326758, 2258910, 6154926

Offset

1,2

Comments

a(n) is an increasing (but not necessarily strictly increasing) sequence.

a(7) = 4849 if all numbers were distinct.

By A238507, a(10) <= 200633.

a(15) > 10^7. - Delbert L. Johnson, Apr 13 2024

Links

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

Example

3^8 = 6561 contains a subsequence of the infinite string in the definition ('56'). Thus a(2) = 8.

Prog

(Python)
def a(n):
  for k in range(1, 10**5):
    for i in range(10):
      s = ''
      for j in range(i, i+n):
        dig=j%10
        s+=str(dig)
      if str(3**k).find(s) > -1:
        return k
n=1
while n < 10:
  print(a(n))
  n+=1

Crossrefs

Cf. A238507.

Sequence in context: A362906 A350442 A151792 * A118526 A167340 A037377

Adjacent sequences: A243292 A243293 A243294 * A243296 A243297 A243298

Keyword

nonn,hard,base,more

Author

Derek Orr, Jun 02 2014

Extensions

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

a(13) from Chai Wah Wu, Jun 14 2020

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

Status

approved