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A309904 Approximation of the 7-adic integer exp(7) up to 7^n. 4


%S 0,1,8,204,890,890,51311,286609,3580781,20875184,182289612,747240110,

%T 8656547082,8656547082,105545557489,783768630338,15026453160167,

%U 114725244868970,1045247300817798,9187315290370043,20586210475743186,20586210475743186

%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 A309905(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. A309905.

%Y The 7-adic expansion of exp(7) is given by A309987.

%Y Approximations of exp(p) in p-adic field: A309900 (p=3), A309902 (p=5), this sequence (p=7).

%K nonn

%O 0,3

%A _Jianing Song_, Aug 21 2019

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Last modified August 1 03:52 EDT 2021. Contains 346384 sequences. (Running on oeis4.)