A010876 a(n) = n mod 7.
0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1).
Programs
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Magma
&cat [[0..6]^^20]; // Bruno Berselli, Jun 09 2016
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PARI
a(n)=n%7 \\ Charles R Greathouse IV, Dec 05 2011
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Sage
[power_mod(n,7,7) for n in range(0, 81)] # Zerinvary Lajos, Nov 07 2009
Formula
Complex representation: a(n) = (1/7)*(1-r^n) * Sum_{1<=k<7} k * Product_{1<=m<7, m<>k} (1-r^(n-m)) where r=exp(2*pi/7*i) and i=sqrt(-1).
Trigonometric representation: a(n) = (64/7)^2*(sin(n*pi/7))^2*Sum_{1<=k<7} k*Product_{1<=m<7,m<>k} sin((n-m)*pi/7)^2.
G.f.: ( Sum_{1<=k<7} k*x^k ) / (1 - x^7).
G.f.: x*(6*x^7-7*x^6+1)/((1-x^7)*(1-x)^2). - Hieronymus Fischer, May 31 2007
a(n) = floor(41152/3333333*10^(n+1)) mod 10. - Hieronymus Fischer, Jan 03 2013
a(n) = floor(7625/274514*7^(n+1)) mod 7. - Hieronymus Fischer, Jan 04 2013
Extensions
Formula section re-edited for better readability by Hieronymus Fischer, Dec 05 2011