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A309453
The successive approximations up to 7^n for 7-adic integer 5^(1/5).
10
0, 3, 45, 339, 1368, 8571, 42185, 630430, 4748145, 27807349, 27807349, 1722658843, 13586619301, 41269193703, 235047214517, 2269716433064, 30755085492722, 230152668910328, 928044210871949, 2556457808782398, 36753143364901827, 196337675960125829, 2430521132293261857
OFFSET
0,2
FORMULA
a(0) = 0 and a(1) = 3, a(n) = a(n-1) + (a(n-1)^5 - 5) mod 7^n for n > 1.
EXAMPLE
a(1) = ( 3)_7 = 3,
a(2) = ( 63)_7 = 45,
a(3) = ( 663)_7 = 339,
a(4) = (3663)_7 = 1368.
PROG
(PARI) {a(n) = truncate((5+O(7^n))^(1/5))}
CROSSREFS
Cf. A309448.
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));
A309452 (7-adic, 4^(1/5));
A309454 (7-adic, 6^(1/5)).
Sequence in context: A370954 A117972 A061532 * A360716 A060242 A271236
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 03 2019
STATUS
approved