A306552 Expansion of the 10-adic cube root of -1/7, that is, the 10-adic integer solution to x^3 = -1/7.

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

Offset

1,1

Comments

10's complement of A319739.

Links

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

Formula

a(n) = 9 - A319739(n) for n >= 2.

Example

3^3 == 7 == -1/7 (mod 10).
93^3 == 57 == -1/7 (mod 100).
593^3 == 857 == -1/7 (mod 1000).
5593^3 == 2857 == -1/7 (mod 10000).
...
...619383045593^3 = ...142857142857 = ...999999999999/7 = -1/7.

Maple

op([1, 3], padic:-rootp(7*x^3+1, 10, 100)); # Robert Israel, Mar 31 2019

Prog

(PARI) seq(n)={Vecrev(digits(lift(chinese( Mod((-1/7 + O(5^n))^(1/3), 5^n), Mod((-1/7 + 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: this sequence (p=-1), A319739 (p=1);

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

q=11: A306553 (p=-1), A319740 (p=1);

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

Sequence in context: A245719 A085851 A212321 * A092041 A317904 A320960

Adjacent sequences: A306549 A306550 A306551 * A306553 A306554 A306555

Keyword

nonn,base

Author

Jianing Song, Feb 23 2019

Status

approved