%I #9 Aug 26 2019 11:23:47

%S 0,1,4,13,67,229,229,958,958,7519,27202,27202,204349,1267231,1267231,

%T 10833169,39530983,125624425,125624425,125624425,1287885892,

%U 4774670293,15235023496,46616083105,140759261932,140759261932,988047871375,3529913699704,11155511184691

%N Approximation of the 3-adic integer exp(3) up to 3^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 A309901(n) modulo 3^n.

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

%o (PARI) a(n) = lift(exp(3 + O(3^n)))

%Y Cf. A309901.

%Y The 3-adic expansion of exp(3) is given by A317675.

%Y Approximations of exp(p) in p-adic field: this sequence (p=3), A309902 (p=5), A309904 (p=7).

%K nonn

%O 0,3

%A _Jianing Song_, Aug 21 2019