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Search: id:A014824
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| A014824 |
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a(0) = 0, a(n) = 10*a(n-1) + n. |
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+0
12
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| 0, 1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 123456789, 1234567900, 12345679011, 123456790122, 1234567901233, 12345679012344, 123456790123455, 1234567901234566, 12345679012345677
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The square roots of these numbers have some remarkable properties - see the link to Schizophrenic numbers.
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LINKS
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K. S. Brown, Schizophrenic numbers
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FORMULA
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a(n) =(10^n-1)*(10/81)-n/9 - Henry Bottomley (se16(AT)btinternet.com), Jul 04 2000
a(n)/10^n converges to 10/81=0.123456790123456790...
Let b(n)=if(n=0, 1, if(n=1, 10, 10*9^(n-2))). Then a(n)=sum{k=0..n, C(n, k)b(k)} (Binomial transform) - Paul Barry (pbarry(AT)wit.ie), Jan 29 2004
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MAPLE
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a:=n->sum((10^(n-j)-1^(n-j))/9, j=0..n): seq(a(n), n=0..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 15 2007
a:=n->sum(10^(n-j)*j, j=0..n): seq(a(n), n=0..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 05 2008
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MATHEMATICA
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Table[Sum[10^i - 1, {i, n}]/9, {n, 18}] (from Robert G. Wilson v Nov 20 2004)
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CROSSREFS
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Cf. A007908, A060011.
Sequence in context: A037610 A035239 A057137 this_sequence A060555 A138957 A007908
Adjacent sequences: A014821 A014822 A014823 this_sequence A014825 A014826 A014827
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KEYWORD
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nonn
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AUTHOR
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njas
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