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Search: id:A010888
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| A010888 |
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Digital root of n (repeatedly add digits until reach a single digit). |
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+0
84
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| 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Decimal expansion of 13717421/111111111 is 0.123456789123456789123456789... with period 9. - Eric Desbiaux (moongerms(AT)wanadoo.fr), May 19 2008
Partial sums are given by A130487(n-1)+n (for n>0). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 08 2007
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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If n=0 then a(n) = 0; otherwise a(n) = (n reduced mod 9), but if the answer is 0 change it to 9.
Equivalently, if n=0 then a(n) = 0, otherwise a(n) = (n-1 reduced mod 9) + 1.
Has period 9.
a(n)=A010878(n-1)+1 (for n>0). - G.f.: g(x)=(x*sum{0<=k<9, (k+1)*x^k})/(1-x^9). Also: g(x)=x(9x^10-10x^9+1)/((1-x^9)(1-x)^2). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 08 2007
a(n) = 1+[(n+8) mod 9]-9*{1-[((n+1)!+1) mod (n+1)]}, with n>=0. a(n) = 1+[(n+8) mod 9]-9*A000007 - Paolo P. Lava (ppl(AT)spl.at), Jun 20 2007
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EXAMPLE
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37 -> 10 -> 1, so a(37)=1.
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MAPLE
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P:=proc(n) local a, i; for i from 0 by 1 to n do a:=1+((i+8) mod 9)-9*(1-(((i+1)!+1) mod (i+1))); print(a); od; end: P(100); - Paolo P. Lava (ppl(AT)spl.at), Jun 20 2007
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MATHEMATICA
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Join[{0}, Array[Mod[ # - 1, 9] + 1 &, 104]] (from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 04 2006)
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CROSSREFS
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Cf. A007953, A007954, A031347, A113217, A113218.
Cf. A010872, A010873, A010874, A010875, A010876, A010877, A010879, A004526, A002264, A002265, A002266.
Sequence in context: A037265 A053837 A128244 this_sequence A131650 A033930 A076314
Adjacent sequences: A010885 A010886 A010887 this_sequence A010889 A010890 A010891
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KEYWORD
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nonn,easy,nice,base
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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