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A309905 Approximation of the 7-adic integer exp(-7) up to 7^n. 4


%S 0,1,43,190,1562,6364,56785,645030,3115659,14645261,14645261,

%T 297120510,8206427482,22047714683,118936725090,118936725090,

%U 23856744274805,123555535983608,588816563958022,5474057357689369,51069638099181941,51069638099181941

%N Approximation of the 7-adic integer exp(-7) up to 7^n.

%C In p-adic field, the exponential function exp(x) is defined as Sum_{k>=0} x^k/k!. When extended to a function over the metric completion of the p-adic field, exp(x) has radius of convergence p^(-1/(p-1)) (i.e., exp(x) converges for x such that |x|_p < p^(-1/(p-1)), where |x|_p is the p-adic metric). As a result, for odd primes p, exp(p) is well-defined in p-adic field, and exp(4) is well defined in 2-adic field.

%C a(n) is the multiplicative inverse of A309904(n) modulo 7^n.

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

%o (PARI) a(n) = lift(exp(-7 + O(7^n)))

%Y Cf. A309904.

%Y The 7-adic expansion of exp(-7) is given by A309988.

%Y Approximations of exp(-p) in p-adic field: A309901 (p=3), A309903 (p=5), this sequence (p=7).

%K nonn

%O 0,3

%A _Jianing Song_, Aug 21 2019

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Last modified March 7 12:19 EST 2021. Contains 341885 sequences. (Running on oeis4.)