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If any power of 2 ends with k 8's and 9's, they must be the first k terms of this sequence in reverse order.
5

%I #42 Jul 22 2024 00:58:36

%S 8,8,8,9,8,9,9,8,9,8,9,8,8,9,9,8,9,8,9,9,9,8,8,8,8,9,8,8,8,8,9,9,9,9,

%T 8,9,8,8,9,9,8,8,9,9,8,9,8,8,9,8,9,8,9,8,8,8,8,8,8,9,9,9,9,8,9,8,8,8,

%U 9,9,8,8,9,8,8,9,9,8,8,9,9,9,8,9,9,9,9,9,9,8,8,9,8,8,9,9,9,9,9,9,8,8,8,9,9,8,8,8

%N If any power of 2 ends with k 8's and 9's, they must be the first k terms of this sequence in reverse order.

%C Upper limit of backward value of 2^n and n!. - _Simon Plouffe_, Mar 23 2009

%H Ray Chandler, <a href="/A023415/b023415.txt">Table of n, a(n) for n = 1..10000</a>

%o (Python)

%o # upper limit of backward value of 2^n

%o a,i=8,0; x=a

%o while i < 200:

%o i+=1; print(x, end=',')

%o if a%2**(i+1) == 0: x=8

%o else: x=9

%o a+=x*10**i

%o # _Cezary Glowacz_, Mar 11 2017

%Y Cf. A145679.

%K nonn,base

%O 1,1

%A _David W. Wilson_