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Search: id:A101291
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| A101291 |
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Sum of all numbers with n digits. |
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+0
6
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| 45, 4905, 494550, 49495500, 4949955000, 494999550000, 49499995500000, 4949999955000000, 494999999550000000, 49499999995500000000, 4949999999955000000000, 494999999999550000000000
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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All terms are multiple of 45: A101291 = 45*(1, 109, 10990, 1099900, 109999000,...), cf. formula. [From M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 26 2008]
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FORMULA
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sum(x, x=1..9), sum(x, x=10..99), sum(x, x=100..999), sum(x, x=1000..9999), sum(x, x=10000..99999), sum(x, x=100000..999999), sum(x, x=1000000..9999999), sum(x, x=10000000..99999999);
a(n) = 99*100^n/200 - 9*10^n/20 = (99*100^n - 90*10^n)/200 = 9*(11*10^(n-1) - 1)*10^(n-1)/2 = 45*(11*10^(2n-3) - 10^(n-2)) [From M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 26 2008]
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EXAMPLE
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a(1) = 1+2+3+4+5+6+7+8+9 = 45
a(2) = 10+11+12+13+14+ ... +97+98+99 = 4905
a(3) = 100+101+102+103+ ... + 997+998+999 = 494550
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MAPLE
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sum(x, x=1..9), sum(x, x=10..99), sum(x, x=100..999), sum(x, x=1000..9999), sum(x, x=10000..99999), sum(x, x=100000..999999), sum(x, x=1000000..9999999), sum(x, x=10000000..99999999);
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MATHEMATICA
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f[n_] := 10^n(10^n - 1)/2; Table[ f[n] - f[n - 1], {n, 12}] (from Robert G. Wilson v Dec 24 2004)
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PROGRAM
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(PARI) A101291(n)=(n=10^(n-1))*(11*n-1)\2*9 [From M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 26 2008]
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CROSSREFS
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First differences of A037182.
Sequence in context: A004707 A036521 A093533 this_sequence A061542 A037182 A134229
Adjacent sequences: A101288 A101289 A101290 this_sequence A101292 A101293 A101294
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KEYWORD
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nonn,base,easy
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AUTHOR
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Jorge Coveiro (jorgecoveiro(AT)yahoo.com), Dec 21 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 24 2004
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