A309766 Digits of the 2-adic integer arctan(4).

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

Offset

0

Comments

arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...

Links

Table of n, a(n) for n=0..87.

Wikipedia, p-adic number

Formula

a(n) = (A309756(n+1) - A309756(n))/2^n.

Example

arctan(4) = ...0100000001010001001111101100100101000100.

Prog

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

Crossrefs

Cf. A309752, A309756, A309768.

Sequence in context: A188079 A049320 A284817 * A354033 A328979 A358227

Adjacent sequences: A309763 A309764 A309765 * A309767 A309768 A309769

Keyword

nonn,base

Author

Jianing Song, Aug 16 2019

Status

approved