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A309452
The successive approximations up to 7^n for 7-adic integer 4^(1/5).
10
0, 2, 9, 107, 450, 450, 67678, 655923, 2303009, 13832611, 54186218, 1749037712, 13612998170, 27454285371, 124343295778, 4193681732872, 18436366262701, 217833949680307, 1380986519616342, 3009400117526791, 3009400117526791, 162593932712750793, 3513869117212454835
OFFSET
0,2
FORMULA
a(0) = 0 and a(1) = 2, a(n) = a(n-1) + 2 * (a(n-1)^5 - 4) mod 7^n for n > 1.
EXAMPLE
a(1) = ( 2)_7 = 2,
a(2) = ( 12)_7 = 9,
a(3) = ( 212)_7 = 107,
a(4) = (1212)_7 = 450.
PROG
(PARI) {a(n) = truncate((4+O(7^n))^(1/5))}
CROSSREFS
Cf. A309447.
Expansions of p-adic integers:
A290800, A290802 (7-adic, sqrt(-6));
A290806, A290809 (7-adic, sqrt(-5));
A290803, A290804 (7-adic, sqrt(-3));
A210852, A212153 (7-adic, (1+sqrt(-3))/2);
A290557, A290559 (7-adic, sqrt(2));
A309450 (7-adic, 2^(1/5));
A309451 (7-adic, 3^(1/5));
A309453 (7-adic, 5^(1/5));
A309454 (7-adic, 6^(1/5)).
Sequence in context: A136172 A012986 A341056 * A354663 A219116 A245731
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 03 2019
STATUS
approved