A321081 Digits of the 2-adic integer log_5(-3).

1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1

Offset: 0

Author

Jianing Song, Oct 27 2018

Keywords

• nonn
• base

Comments

See A321080 for the definition of log_5(-3) and more information.

Multiplicative inverse of A321083.

Examples

			log_5(-3) = ...1000011001011001010001001010011010100011.
		

Links

• Jianing Song, Table of n, a(n) for n = 0..1000
• Wikipedia, p-adic number

Crossrefs

Cf. A321080, A321083, A321694.

Programs

PARI

b(n) = {my(v=vector(n)); v[2]=0; for(n=3, n, v[n] = v[n-1] + if(Mod(5,2^n)^v[n-1] + 3==0, 0, 2^(n-3))); v}
a(n) = b(n+3)[n+3]\2^n

Formula

a(n) = 0 if 5^A321080(n+2) + 3 is divisible by 2^(n+3), otherwise 1.

Equals to A321694/A152228.