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A309754 Digits of the 2-adic integer arctanh(2). 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 5 00:15 EDT 2021. Contains 346456 sequences. (Running on oeis4.)