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

Author

Derek Orr, Jun 02 2014

Keywords

• nonn
• hard
• base
• more

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

Examples

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

Crossrefs

Cf. A238507.

Programs

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

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