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A309847 Digits of the multiplicative inverse of A309752. 1
1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
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)} (-1)^i*2^(2*i)/(2*i+1)) == 1 (mod 2^(n+2)).

EXAMPLE

arctan(2) = ...0101100110111010110101111110001011001010, so 1/arctan(2) = ...100010111110000010011001110110000110110.1.

PROG

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

CROSSREFS

Cf. A309752, A309848.

Sequence in context: A005614 A267605 A319843 * A266786 A272532 A166946

Adjacent sequences:  A309844 A309845 A309846 * A309848 A309849 A309850

KEYWORD

nonn,base

AUTHOR

Jianing Song, Aug 20 2019

STATUS

approved

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Last modified February 25 23:44 EST 2020. Contains 332270 sequences. (Running on oeis4.)