A309849 Digits of the multiplicative inverse of A309766.

1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 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)} (-1)^i*4^(2*i)/(2*i+1)) == 1 (mod 2^(n+3)).

Example

arctan(4) = ...0100000001010001001111101100100101000100, so 1/arctan(4) = ...00010111001111001111011011010110101100.01.

Prog

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

Crossrefs

Cf. A309766, A309850.

Sequence in context: A088592 A188189 A029692 * A071906 A104107 A120532

Adjacent sequences: A309846 A309847 A309848 * A309850 A309851 A309852

Keyword

nonn,base

Author

Jianing Song, Aug 20 2019

Status

approved