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Search: id:A096005
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| A096005 |
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For k >= 1, let b(k) = ceiling( Sum_{i=1..k} 1/i ); a(n) = number of b(k) that are equal to n. |
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1
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| 0, 1, 2, 7, 20, 52, 144, 389, 1058, 2876, 7817, 21250, 57763, 157017, 426817, 1160207, 3153770, 8572836, 23303385, 63345169, 172190019, 468061001, 1272321714, 3458528995, 9401256521, 25555264765, 69466411833, 188829284972
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n+1)/a(n) approaches e = exp(1) = 2.71828...
First differences of A002387. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 30 2004
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EXAMPLE
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The ceilings of the first several partial sums of the reciprocal of the positive integers are 1 2 2 3 3 3 3 3 3 3 4 4 and the series is monotonically increasing, so a(0) = 0 (there being no zero), a(1) = 1 (there being but one 1) and a(3) = 7 (there being seven 3s).
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MATHEMATICA
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fh[0] = 0; fh[1] = 1; fh[k_] := Module[{tmp}, If[ Floor[tmp = Log[k + 1/2] + EulerGamma] == Floor[tmp + 1/(24k^2)], Floor[tmp], UNKNOWN]]; a[0] = 1; a[1] = 2; a[n_] := Module[{val}, val = Round[Exp[n - EulerGamma]]; If[fh[val] == n && fh[val - 1] == n - 1, val, UNKNOWN]]; Table[ a[n + 1] - a[n], {n, 0, 27}] (from Robert G. Wilson v Aug 05 2004)
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CROSSREFS
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Cf. A002387, A096143.
Adjacent sequences: A096002 A096003 A096004 this_sequence A096006 A096007 A096008
Sequence in context: A123203 A134311 A066373 this_sequence A050532 A050513 A128183
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KEYWORD
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easy,nonn
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AUTHOR
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Neville Holmes (neville.holmes(AT)utas.edu.au), Jul 29 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 05 2004
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