A243150 Least number k > 0 such that 2^k contains an n-digit long substring of the infinite string "0123456789012345678901234567890123456....".

1, 7, 28, 106, 391, 992, 1178, 7255, 15975, 67143, 333212, 333212, 1641257

Offset: 1

Author

Derek Orr, May 31 2014

Keywords

• nonn
• more
• hard
• base

Comments

By A238448, a(10) <= 244178.

Examples

			2^7 = 128 contains the 2-digit substring "12". Thus a(2) = 7.
		

Crossrefs

Cf. A238448.

Programs

Python

import sys
sys.set_int_max_str_digits(5000)
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(2**k).find(s) > -1:
        return k
n=1
while n < 10:
  print(a(n))
  n+=1

Extensions

a(10)-a(13) from Hiroaki Yamanouchi, Sep 26 2014