A309848 Digits of the multiplicative inverse of A309754.

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

Offset

-1

Links

Table of n, a(n) for n=-1..86.

Wikipedia, p-adic number

Formula

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

Example

arctanh(2) = ...0111000110010001010010010111010001111010, so 1/arctanh(2) = 010110010000100011000000001011010001010.1.

Prog

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

Crossrefs

Cf. A309754, A309847.

Sequence in context: A085405 A036988 A108357 * A326822 A088517 A325897

Adjacent sequences: A309845 A309846 A309847 * A309849 A309850 A309851

Keyword

nonn,base

Author

Jianing Song, Aug 20 2019

Status

approved