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Digits of the 2-adic integer exp(-4).
2

%I #5 Nov 18 2018 10:04:26

%S 1,0,1,0,0,0,0,1,1,1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,

%T 0,0,0,1,1,0,0,1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,

%U 0,1,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,0,0

%N Digits of the 2-adic integer exp(-4).

%C This is the multiplicative inverse of A320815.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>

%F a(n) = (A321689(n+1) - A321689(n))/2^n.

%e exp(-4) = ...00110000100100101000011101101111110000101.

%o (PARI) a(n) = lift(sum(i=0, n-(n>=2), Mod(4^i/i!, 2^(n+1))))\2^n

%o (PARI) a(n) = lift(exp(-4 + O(2^(n+1))))\2^n;

%Y Cf. A320815, A321689.

%K nonn,base

%O 0,1

%A _Jianing Song_, Nov 17 2018