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A309849 Digits of the multiplicative inverse of A309766. 1
1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

-2

LINKS

Table of n, a(n) for n=-2..85.

Wikipedia, p-adic number

FORMULA

By definition, (Sum_{i=-2..n} a(i)*2^(i+2)) * (Sum_{i=0..floor((n+2)/4)} (-1)^i*4^(2*i)/(2*i+1)) == 1 (mod 2^(n+3)).

EXAMPLE

arctan(4) = ...0100000001010001001111101100100101000100, so 1/arctan(4) = ...00010111001111001111011011010110101100.01.

PROG

(PARI) a(n) = lift(Mod(sum(i=0, (n+2)/4, (-1)^i*4^(2*i)/(2*i+1)), 2^(n+3))^(-1))\2^(n+2)

CROSSREFS

Cf. A309766, A309850.

Sequence in context: A088592 A188189 A029692 * A071906 A104107 A120532

Adjacent sequences:  A309845 A309847 A309848 * A309850 A309851 A309852

KEYWORD

nonn,base

AUTHOR

Jianing Song, Aug 20 2019

STATUS

approved

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Last modified November 18 22:39 EST 2019. Contains 329305 sequences. (Running on oeis4.)