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A193345 Digits occurring in A173616. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

LINKS

Table of n, a(n) for n=1..86.

EXAMPLE

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).

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}]

PROG

(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)

CROSSREFS

Sequence in context: A244263 A288023 A020506 * A197822 A055060 A010515

Adjacent sequences: A193342 A193343 A193344 * A193346 A193347 A193348

KEYWORD

nonn,base,easy

AUTHOR

José María Grau Ribas, Jul 23 2011

EXTENSIONS

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

STATUS

approved

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Last modified February 2 21:10 EST 2023. Contains 360024 sequences. (Running on oeis4.)