A133880 n modulo p repeated p times (where p=10).

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

Offset: 0

Author

Hieronymus Fischer, Oct 10 2007

Keywords

• nonn
• easy

Comments

Periodic with length p^2=100.

a(n) = A179051(n) for n < 90. - Reinhard Zumkeller, Jun 27 2010

Links

• Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1).

Crossrefs

Cf. A000040, A133620-A133625, A133630, A038509, A133634-A133636.

Cf. A133890, A133900, A133910.

Programs

Mathematica

Flatten[Table[PadRight[{},10,Mod[n,10]],{n,11}]] (* Harvey P. Dale, May 10 2012 *)

PARI

a(n)=(n\10+1)%10 \\ Charles R Greathouse IV, Nov 15 2022

Formula

The following formulas are given for a general parameter p (p=10 for this sequence).

a(n)=(1+floor(n/p)) mod p.

a(n)=1+floor(n/p)-p*floor((n+p)/p^2).

a(n)=(((n+p) mod p^2)-(n mod p))/p.

a(n)=((n+p-(n mod p))/p) mod p.

G.f. g(x)=((p-1)x^(p^2)-px^(p(p-1))+1)/((1-x)(1-x^p)(1-x^(p^2))).

G.f. g(x)=(1-x^p)*sum{0<=k<(p-1), (k+1)*x^(k*p)}/((1-x)(1-x^(p^2))).