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A010877
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a(n) = n mod 8.
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37
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0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0
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OFFSET
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0,3
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COMMENTS
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The rightmost digit in the base-8 representation of n. Also, the equivalent value of the three rightmost digits in the base-2 representation of n. - Hieronymus Fischer, Jun 12 2007
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 0..65536
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1).
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FORMULA
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Complex representation: a(n) = (1/8)*(1-r^n)*Sum_{k=1..7} k*Product_{m=1..7, m<>k} (1 - r^(n-m)) where r = exp(Pi/4*i) = (1+i)*sqrt(2)/2 and i=sqrt(-1).
Trigonometric representation: a(n) = 256*(sin(n*Pi/8))^2*Sum_{k=1..7} k*Product_{m=1..7, m<>k} (sin((n-m)*Pi/8))^2.
G.f.: g(x) = (Sum_{k=1..7}, k*x^k)/(1-x^8).
Also: g(x) = x(7x^8-8x^7+1)/((1-x^8)(1-x)^2). - Hieronymus Fischer, May 31 2007
a(n) = n mod 2 + 2*(floor(n/2) mod 4) = A000035(n) + 2*A010873(A004526(n)).
a(n) = n mod 4 + 4*(floor(n/4) mod 2) = A010873(n) + 4*A000035(A002265(n)).
a(n) = n mod 2 + 2*(floor(n/2) mod 2) + 4*(floor(n/4) mod 2) = A000035(n) + 2*A000035(A004526(n))) + 4*A000035(A002265(n)). - Hieronymus Fischer, Jun 12 2007
a(n) = (1/2)*(7 - (-1)^n - 2*(-1)^(b/4) - 4*(-1)^((b - 2 + 2*(-1)^(b/4))/8)) where b = 2n - 1 + (-1)^n. - Hieronymus Fischer, Jun 12 2007
General formula for period 2^k: a(n) = (1/2)*(2^k - 1 - Sum_{j=0..k-1} 2^j*(-1)^p(j,n)) where p(j,n) is defined recursively by p(0,n)=n, p(j,n) = (1/4)*(2*p(j-1,n) - 1 + (-1)^p(j-1,n)). - Hieronymus Fischer, Jun 14 2007
a(n) = floor(1234567/99999999*10^(n+1)) mod 10. - Hieronymus Fischer, Jan 03 2013
a(n) = floor(48913/2396745*8^(n+1)) mod 8. - Hieronymus Fischer, Jan 04 2013
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MATHEMATICA
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Table[Mod[n, 8], {n, 0, 120}] (* Harvey P. Dale, Apr 21 2011 *)
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PROG
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(PARI) vector(100, i, i)%8 \\ Charles R Greathouse IV, Jul 16, 2011
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CROSSREFS
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Partial sums: A130486. Other related sequences A130481, A130482, A130483, A130484, A130485.
Cf. A000035, A010887, A130909, A010873, A130909, A168181, A244413, A253513.
Sequence in context: A037850 A037886 A031045 * A257848 A195831 A265521
Adjacent sequences: A010874 A010875 A010876 * A010878 A010879 A010880
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Formula section re-edited for better readability by Hieronymus Fischer
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STATUS
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approved
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