

A309903


Approximation of the 5adic integer exp(5) up to 5^n.


4



0, 1, 21, 71, 196, 2071, 2071, 33321, 345821, 736446, 8548946, 18314571, 18314571, 994877071, 994877071, 25408939571, 86444095821, 239031986446, 1001971439571, 16260760502071, 92554705814571, 283289569095821, 1236963885502071, 8389521258548946
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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 A309902(n) modulo 5^n.


LINKS

Table of n, a(n) for n=0..23.
Wikipedia, padic number


PROG

(PARI) a(n) = lift(exp(5 + O(5^n)))


CROSSREFS

Cf. A309902.
The 5adic expansion of exp(5) is given by A309975.
Approximations of exp(p) in padic field: A309901 (p=3), this sequence (p=5), A309905 (p=7).
Sequence in context: A195026 A296035 A102233 * A187719 A156285 A160435
Adjacent sequences: A309900 A309901 A309902 * A309904 A309905 A309906


KEYWORD

nonn


AUTHOR

Jianing Song, Aug 21 2019


STATUS

approved



