A309847 Digits of the multiplicative inverse of A309752.

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

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)} (-1)^i*2^(2*i)/(2*i+1)) == 1 (mod 2^(n+2)).

Example

arctan(2) = ...0101100110111010110101111110001011001010, so 1/arctan(2) = ...100010111110000010011001110110000110110.1.

Prog

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

Crossrefs

Cf. A309752, A309848.

Sequence in context: A267605 A373550 A319843 * A266786 A272532 A166946

Adjacent sequences: A309844 A309845 A309846 * A309848 A309849 A309850

Keyword

nonn,base

Author

Jianing Song, Aug 20 2019

Status

approved