|
%I #23 May 29 2020 19:16:10
%S 1,5,25,78,161,341,1076,16361,19383,56047,132903,862935,862935,4381548
%N Least number k > 0 such that 2^k contains an n-digit long substring of the infinite string "98765432109876543210987654..."
%C a(n+1) >= a(n) for all n.
%e 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.
%o (Python)
%o def Rev(n):
%o ..rev = ''
%o ..for i in str(n):
%o ....rev = i + rev
%o ..return rev
%o def a(n):
%o ..lst = []
%o ..for b in range(1,10**n):
%o ....if len(str(2**b)) >= n:
%o ......lst.append(b)
%o ......break
%o ..for k in range(lst[0],50000):
%o ....for i in range(10):
%o ......s = ''
%o ......s += str(i)
%o ......for j in range(i+1,i+n):
%o ........dig = j%10
%o ........s+=str(dig)
%o ......if str(2**k).find(Rev(s)) > -1:
%o ........return k
%o n = 1
%o while n < 100:
%o ..print(a(n),end=', ')
%o ..n += 1
%Y Cf. A243150.
%K nonn,base,hard,more
%O 1,2
%A _Derek Orr_, Jun 04 2014
%E a(10)-a(13) from _Hiroaki Yamanouchi_, Sep 26 2014
%E a(14) from _Chai Wah Wu_, May 29 2020
| 