A309850 Digits of the multiplicative inverse of A309768.

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

Offset

-2

Links

Table of n, a(n) for n=-2..85.

Wikipedia, p-adic number

Formula

By definition, (Sum_{i=-2..n} a(i)*2^(i+2)) * (Sum_{i=0..floor((n+2)/4)} 4^(2*i)/(2*i+1)) == 1 (mod 2^(n+3)).

Example

arctanh(4) = ...0100000010101110111011111001111011000100, so 1/arctanh(4) = ...10110110010101001110010000000001010100.01.

Prog

(PARI) a(n) = lift(Mod(sum(i=0, (n+2)/4, 4^(2*i)/(2*i+1)), 2^(n+3))^(-1))\2^(n+2)

Crossrefs

Cf. A309768, A309849.

Sequence in context: A168553 A267636 A267841 * A262448 A068430 A141738

Adjacent sequences: A309847 A309848 A309849 * A309851 A309852 A309853

Keyword

nonn

Author

Jianing Song, Aug 20 2019

Status

approved