A225455 10-adic integer x such that x^9 == (10^n-1)/9 mod 10^n for all n.

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

Offset: 1

Author

Aswini Vaidyanathan, May 11 2013

Keywords

• nonn
• base

Examples

			1^9 == 1 (mod 10).
91^9 == 11 (mod 100).
391^9 == 111 (mod 1000).
4391^9 == 1111 (mod 10000).
84391^9 == 11111 (mod 100000).
584391^9 == 111111 (mod 1000000).
		

Links

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

Programs

Maple

A[1]:= 1: P:= 1:
for d from 2 to 100 do
  R:= (expand((10^(d-1)*x+P)^9 - ((10^d-1)/9)) mod 10^d)/10^(d-1);
  A[d]:= subs(msolve(R,10),x);
  P:= subs(10^(d-1)*A[d]+P);
od:
seq(A[i],i=1..100); # Robert Israel, Oct 03 2018

PARI

n=0;for(i=1,100,m=(10^i-1)/9;for(x=0,9,if(((n+(x*10^(i-1)))^9)%(10^i)==m,n=n+(x*10^(i-1));print1(x", ");break)))