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