

A309904


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


4



0, 1, 8, 204, 890, 890, 51311, 286609, 3580781, 20875184, 182289612, 747240110, 8656547082, 8656547082, 105545557489, 783768630338, 15026453160167, 114725244868970, 1045247300817798, 9187315290370043, 20586210475743186, 20586210475743186
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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 A309905(n) modulo 7^n.


LINKS

Table of n, a(n) for n=0..21.
Wikipedia, padic number


PROG

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


CROSSREFS

Cf. A309905.
The 7adic expansion of exp(7) is given by A309987.
Approximations of exp(p) in padic field: A309900 (p=3), A309902 (p=5), this sequence (p=7).
Sequence in context: A221121 A264124 A317631 * A241224 A259065 A204247
Adjacent sequences: A309901 A309902 A309903 * A309905 A309906 A309907


KEYWORD

nonn


AUTHOR

Jianing Song, Aug 21 2019


STATUS

approved



