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

Offset

1,2

Links

Table of n, a(n) for n=1..22.

Formula

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

Prog

(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

Crossrefs

Cf. A053312

Sequence in context: A231155 A376145 A279166 * A178369 A328492 A306686

Adjacent sequences: A147881 A147882 A147883 * A147885 A147886 A147887

Keyword

base,easy,nonn

Author

Max Alekseyev, Nov 17 2008

Status

approved