

A309900


Approximation of the 3adic integer exp(3) up to 3^n.


3



0, 1, 4, 13, 67, 229, 229, 958, 958, 7519, 27202, 27202, 204349, 1267231, 1267231, 10833169, 39530983, 125624425, 125624425, 125624425, 1287885892, 4774670293, 15235023496, 46616083105, 140759261932, 140759261932, 988047871375, 3529913699704, 11155511184691
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OFFSET

0,3


COMMENTS

In padic 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 padic field, exp(x) has radius of convergence p^(1/(p1)) (i.e., exp(x) converges for x such that x_p < p^(1/(p1)), where x_p is the padic metric). As a result, for odd primes p, exp(p) is welldefined in padic field, and exp(4) is well defined in 2adic field.
a(n) is the multiplicative inverse of A309901(n) modulo 3^n.


LINKS

Table of n, a(n) for n=0..28.
Wikipedia, padic number


PROG

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


CROSSREFS

Cf. A309901.
The 3adic expansion of exp(3) is given by A317675.
Approximations of exp(p) in padic field: this sequence (p=3), A309902 (p=5), A309904 (p=7).
Sequence in context: A129433 A157311 A318600 * A096805 A009221 A009239
Adjacent sequences: A309897 A309898 A309899 * A309901 A309902 A309903


KEYWORD

nonn


AUTHOR

Jianing Song, Aug 21 2019


STATUS

approved



