A306553 Expansion of the 10-adic cube root of -1/11, that is, the 10-adic integer solution to x^3 = -1/11.

9, 6, 8, 2, 3, 8, 1, 4, 2, 0, 2, 0, 6, 9, 8, 3, 8, 9, 4, 5, 4, 0, 6, 0, 0, 9, 6, 8, 6, 1, 3, 4, 7, 8, 0, 6, 6, 7, 1, 6, 5, 5, 3, 6, 4, 9, 9, 0, 2, 7, 1, 7, 4, 2, 6, 5, 1, 4, 0, 6, 9, 0, 7, 0, 8, 7, 8, 1, 4, 1, 2, 6, 6, 9, 4, 2, 5, 3, 5, 7, 4, 9, 6, 4, 4, 0, 5

Offset

1,1

Comments

10's complement of A319740.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = 9 - A319740(n) for n >= 2.

Example

9^3 == 9 == -1/11 (mod 10).
69^3 == 9 == -1/11 (mod 100).
869^3 == 909 == -1/11 (mod 1000).
2869^3 == 909 == -1/11 (mod 10000).
...
...020241832869^3 = ...090909090909 = ...999999999999/11 = -1/11.

Maple

op([1, 3], padic:-rootp(11*x^3+1, 10, 100)); # Robert Israel, Mar 24 2019

Prog

(PARI) seq(n)={Vecrev(digits(lift(chinese( Mod((-1/11 + O(5^n))^(1/3), 5^n), Mod((-1/11 + O(2^n))^(1/3), 2^n)))), n)} \\ Following Andrew Howroyd's code for A319740.

Crossrefs

10-adic cube root of p/q:

q=1: A225409 (p=-9), A225408 (p=-7), A225407 (p=-3), A225404 (p=3), A225405 (p=7), A225406 (p=9);

q=3: A225402 (p=-1), A225411 (p=1);

q=7: A306552 (p=-1), A319739 (p=1);

q=9: A225401 (p=-7), A153042 (p=-1), A225412 (p=1), A225410 (p=7);

q=11: this sequence (p=-1), A319740 (p=1);

q=13: A306555 (p=-1), A306554 (p=1).

Sequence in context: A157989 A243265 A248472 * A011194 A235916 A198567

Adjacent sequences: A306550 A306551 A306552 * A306554 A306555 A306556

Keyword

nonn,base

Author

Jianing Song, Feb 23 2019

Status

approved