A309754 Digits of the 2-adic integer arctanh(2).

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

Offset

0

Comments

arctanh(x) = x + x^3/3 + x^5/5 + x^7/7 + ...

Links

Robert Israel, Table of n, a(n) for n = 0..2500

Wikipedia, p-adic number

Formula

a(n) = (A309753(n+1) - A309753(n))/2^n.

Example

arctanh(2) = ...0111000110010001010010010111010001111010.

Maple

N:= 100: # for a(0)..a(N)
T:= 0:
for k from 1 to N by 2 do
  T:= padic:-evalp(T + 2^k/k, 2, N+1)
od:
0, op(op([1, 3], T)); # Robert Israel, Jul 10 2020

Prog

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

Crossrefs

Cf. A309752, A309753.

Sequence in context: A284893 A316829 A277674 * A112690 A316343 A288864

Adjacent sequences: A309751 A309752 A309753 * A309755 A309756 A309757

Keyword

nonn,base

Author

Jianing Song, Aug 15 2019

Status

approved