A243303 Least number k > 0 such that 2^k contains an n-digit long substring of the infinite string "98765432109876543210987654..."

1, 5, 25, 78, 161, 341, 1076, 16361, 19383, 56047, 132903, 862935, 862935, 4381548

Offset

1,2

Comments

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

Links

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

Example

2^25 = 33554432 contains a 3-digit substring of "98765432109876543210987654..." (in this case, "432"). Since 25 is the lower power to have this property, a(3) = 25.

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(2**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(2**k).find(Rev(s)) > -1:
........return k
n = 1
while n < 100:
..print(a(n), end=', ')
..n += 1

Crossrefs

Cf. A243150.

Sequence in context: A301912 A171272 A366158 * A238449 A062989 A122679

Adjacent sequences: A243300 A243301 A243302 * A243304 A243305 A243306

Keyword

nonn,base,hard,more

Author

Derek Orr, Jun 04 2014

Extensions

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

a(14) from Chai Wah Wu, May 29 2020

Status

approved