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A309450
The successive approximations up to 7^n for 7-adic integer 2^(1/5).
11
0, 4, 46, 95, 1124, 15530, 82758, 435705, 4553420, 27612624, 269734266, 1682110511, 9591417483, 9591417483, 9591417483, 4078929854577, 23069175894349, 122767967603152, 1053290023551980, 9195358013104225, 77588729125343083, 237173261720567085, 1354264989887135099
OFFSET
0,2
LINKS
FORMULA
a(0) = 0 and a(1) = 4, a(n) = a(n-1) + (a(n-1)^5 - 2) mod 7^n for n > 1.
EXAMPLE
a(1) = ( 4)_7 = 4,
a(2) = ( 64)_7 = 46,
a(3) = ( 164)_7 = 95,
a(4) = (3164)_7 = 1124.
MAPLE
A:= op([1, 3], padic:-rootp(x^5 -2, 7, 25)):
seq(add(A[i]*10^(i-1), i=1..n), n=0..25); # Robert Israel, Aug 04 2019
PROG
(PARI) {a(n) = truncate((2+O(7^n))^(1/5))}
CROSSREFS
Cf. A309445.
Expansions of p-adic integers:
A290567 (5-adic, 2^(1/3));
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));
A309451 (7-adic, 3^(1/5));
A309452 (7-adic, 4^(1/5));
A309453 (7-adic, 5^(1/5));
A309454 (7-adic, 6^(1/5)).
Sequence in context: A374591 A134110 A176312 * A119046 A273776 A131540
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 03 2019
STATUS
approved