OFFSET
1,2
COMMENTS
For any n there is only one solution. Case a(n)=0 means that cube of (n-1)-digit number ends with n (not (n-1)) 1's. Case a(n+1)=a(n)=0 means that cube of (n-1)-digit number ends with (n+1) (not (n-1)) 1's, etc.
10-adic integer x such that x^3 == (10^n-1)/9 mod 10^n. - Aswini Vaidyanathan, May 07 2013
10-adic digits of the cubic root of -1/9. - Max Alekseyev, Jul 12 2022
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
1^3= 1; 71^3 = 357911; 471^3 = 104487111; 8471^3 = 607860671111.
MAPLE
N:= 200:
op([1, 3], padic:-rootp(9*x^3+1, 10, N+2))[1..N+1]; # Robert Israel, Mar 25 2018
PROG
(PARI) n=0; for(i=1, 100, m=(10^i-1)/9; for(x=0, 9, if(((n+(x*10^(i-1)))^3)%(10^i)==m, n=n+(x*10^(i-1)); print1(x", "); break))) \\ Aswini Vaidyanathan, May 07 2013
(PARI) digits(sqrtn(-1/9 + O(10^100), 3)) \\ Max Alekseyev, Jul 12 2022
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Zak Seidov, Dec 17 2008, corrected Dec 20 2008
STATUS
approved