A309848 - OEIS

A309848

Digits of the multiplicative inverse of A309754.

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

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

EXAMPLE

arctanh(2) = ...0111000110010001010010010111010001111010, so 1/arctanh(2) = 010110010000100011000000001011010001010.1.

PROG

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