A309752 Digits of the 2-adic integer arctan(2).

0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 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..86.

Wikipedia, p-adic number

Formula

a(n) = (A309751(n+1) - A309751(n))/2^n.

Example

arctan(2) = ...0101100110111010110101111110001011001010.

Prog

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

Crossrefs

Cf. A309751, A309754.

Sequence in context: A175992 A173922 A213676 * A209355 A141743 A268384

Adjacent sequences: A309749 A309750 A309751 * A309753 A309754 A309755

Keyword

nonn,base

Author

Jianing Song, Aug 15 2019

Status

approved