A193345 Digits occurring in A173616.

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

Offset: 1

Author

José María Grau Ribas, Jul 23 2011

Keywords

• nonn
• base
• easy

Comments

a(n) = A173616(n) - 10*A173616(n-1).

This is the 10-adic integer x such that x^9 == (10^n-9) mod 10^n for all n. It is the 10's complement of A225458. - Aswini Vaidyanathan, May 11 2013

Examples

			1111^1111=.........8711; 111^111=........711;
10^(1-4)(8711-711)=8 ==> a(4)=8
Comment from _Aswini Vaidyanathan_, May 11 2013:
1^9 == 1 (mod 10).
11^9 == 91 (mod 100).
711^9 == 991 (mod 1000).
8711^9 == 9991 (mod 10000).
78711^9 == 99991 (mod 100000).
78711^9 == 999991 (mod 1000000).
		

Crossrefs

Cf. A173616, A225458.

Programs

Mathematica

repunit[n_] := Sum[10^i, {i,0,n-1}]; a[n_] := 10^(1-n)(PowerMod[repunit[n], repunit[n],10^n] - PowerMod[repunit[n-1], repunit[n-1], 10^(n-1)]); Table[a[n],{n,200}]

PARI

n=0;for(i=1,100,m=(10^i-9);for(x=0,9,if(((n+(x*10^(i-1)))^9)%(10^i)==m,n=n+(x*10^(i-1));print1(x", ");break))) (From Aswini Vaidyanathan, May 11 2013)

Extensions

Edited by N. J. A. Sloane, May 12 2013