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Search: id:A010879
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| 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0
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OFFSET
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0,3
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COMMENT
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Also decimal expansion of 137174210/1111111111 = 0.1234567890123456789012345678901234... - Jason Earls (jcearls(AT)cableone.net), Mar 19 2001
In general the base k expansion of A062808(k)/A048861(k) (k>=2) will produce the numbers 0,1,2,...,k-1 repeated with period k, equivalent to the sequence n mod k. The k-digit number in base k 123...(k-1)0 (base k) expressed in decimal is A062808(k), whereas A048861(k) = k^k-1. In particular, A062808(10)/A048861(10)=1234567890/9999999999=137174210/1111111111.
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LINKS
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Index entries for sequences related to final digits of numbers
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FORMULA
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a(n)=n mod 10
Periodic with period 10.
a(n)=n mod 10. Complex representation: a(n)=1/10*(1-r^n)*sum{1<=k<10, k*product{1<=m<10,m<>k, (1-r^(n-m))}} where r=exp(pi/5*i) and i=sqrt(-1). Trigonometric representation: a(n)=(256/5)^2*(sin(n*pi/10))^2*sum{1<=k<10, k*product{1<=m<10,m<>k, (sin((n-m)*pi/10))^2}}. G.f.: g(x)=(sum{1<=k<10, k*x^k})/(1-x^10). Also: g(x)=x(9x^10-10x^9+1)/((1-x^10)(1-x)^2). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 31 2007
a(n)=n mod 2+2*(floor(n/2)mod 5)=A000035(n)+2*A010874(A004526(n)). Also: a(n)=n mod 5+5*(floor(n/5)mod 2)=A010874(n)+5*A000035(A002266(n)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 11 2007
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CROSSREFS
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Cf. A034948, A059988, A048861, A062808.
Partial sums: A130488. Other related sequences A130481, A130482, A130483, A130484, A130485, A130486, A130487.
Adjacent sequences: A010876 A010877 A010878 this_sequence A010880 A010881 A010882
Sequence in context: A004430 A134778 A118943 this_sequence A062078 A031347 A087471
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KEYWORD
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nonn
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AUTHOR
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njas
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