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A010879
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Final digit of n.
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59
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Also decimal expansion of 137174210/1111111111 = 0.1234567890123456789012345678901234... - Jason Earls (zevi_35711(AT)yahoo.com), 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.
n^5 mod 10. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 04 2009]
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1).
Index entries for sequences related to final digits of numbers
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FORMULA
| a(n)=n mod 10
Periodic with period 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
a(n)=10*{x/10}; Where {x} means fractional part of x [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Jul 30 2009]
a(n) = n - 10*A059995(n). [Reinhard Zumkeller, Jul 26 2011]
[Formula section edited for better readability by Hieronymus Fischer]
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MATHEMATICA
| Table[10*FractionalPart[n/10], {n, 1, 300}] [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Jul 30 2009]
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PROG
| (Other) sage: [power_mod(n, 5, 10)for n in xrange(0, 81)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 04 2009]
(PARI) a(n)=n%10 \\ Charles R Greathouse IV, Jun 16 2011
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CROSSREFS
| Cf. A034948, A059988, A048861, A062808, A086457, A086458.
Partial sums: A130488. Other related sequences A130481, A130482, A130483, A130484, A130485, A130486, A130487.
Sequence in context: A004430 A134778 A118943 * A179636 A175419 A175422
Adjacent sequences: A010876 A010877 A010878 * A010880 A010881 A010882
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KEYWORD
| nonn,base,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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