A147884 - OEIS

%I #7 Mar 16 2023 11:26:04

%S 1,9,89,89,589,3089,3089,3089,315589,315589,8128089,164378089,

%T 945628089,1922190589,11687815589,109344065589,231414378089,

%U 1452117503089,4503875315589,65539031565589,141832976878089,1667711883128089

%N a(n) is the smallest positive integer k such that the last n digits of 2^k are 1 or 2.

%F a(n) = the smallest degree k such that 2^k == A053312(n) (mod 5^n)

%o (PARI) { m=2; for(n=1,50, print1(znlog(m,Mod(2,5^n)),", "); m+=10^n; if(m%(2^(n+1)), m+=10^n); ) }

%o (Python)

%o from itertools import count, islice

%o from sympy import discrete_log

%o def A147884_gen(): # generator of terms

%o     a, b, c = 0, 1, 1

%o     for n in count(0):

%o         a+=b*c if (a>>n)&1 else b*c<<1

%o         c *= 5

%o         yield int(discrete_log(c,a,2))

%o         b <<= 1

%o A147884_list = list(islice(A147884_gen(),20)) # _Chai Wah Wu_, Mar 16 2023

%Y Cf. A053312

%K base,easy,nonn

%O 1,2

%A _Max Alekseyev_, Nov 17 2008