A147884 a(n) is the smallest positive integer k such that the last n digits of 2^k are 1 or 2.

1, 9, 89, 89, 589, 3089, 3089, 3089, 315589, 315589, 8128089, 164378089, 945628089, 1922190589, 11687815589, 109344065589, 231414378089, 1452117503089, 4503875315589, 65539031565589, 141832976878089, 1667711883128089, 3575060515940589

Offset: 1

Author

Max Alekseyev, Nov 17 2008

Keywords

• base
• easy
• nonn

Links

• Minfeng Wang, Table of n, a(n) for n = 1..1429

Crossrefs

Cf. A053312

Programs

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); ) }

Python

from itertools import count, islice
from sympy import discrete_log
def A147884_gen(): # generator of terms
    a, b, c = 0, 1, 1
    for n in count(0):
        a+=b*c if (a>>n)&1 else b*c<<1
        c *= 5
        yield int(discrete_log(c,a,2))
        b <<= 1
A147884_list = list(islice(A147884_gen(),20)) # Chai Wah Wu, Mar 16 2023

Formula

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

Extensions

Extended by Minfeng Wang, Dec 15 2024