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A227513 Round(-1/n + 1/log((2n+1)/(2n-1))). 2
10, 92, 319, 761, 1491, 2581, 4103, 6130, 8732, 11982, 15952, 20714, 26341, 32903, 40473, 49123, 58925, 69952, 82274, 95964, 111094, 127736, 145963, 165845, 187455, 210865, 236147, 263374, 292616, 323946, 357436, 393158, 431185, 471587, 514437, 559807 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

log(u/v), where u = n + 1/2 and v = n - 1/2, is the area under the curve y = 1/x that matches the rectangle of width 1 and height 1/n with base centered at (1/n,0); a(n) -> oo since -1/n + log(u/v) -> 0.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 12*n^3 - round(9*n/5) (conjectured, based on computations by Peter J. C. Moses, Jul 14 2013).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-5) - 3*a(n-6) + 3*a(n-7) - a(n-8) (conjectured; verified up to n = 100000 ).

G.f.: (10 + 62 x + 73 x^2 + 70 x^3 + 73 x^4 + 62 x^5 + 10 x^6)/((-1 + x)^4 (1 + x + x^2 + x^3 + x^4))) (conjectured).

EXAMPLE

-1/4 + log(9/7) = 0.0013144..., so 1/u = 760.78...,so a(4) = 761.

MATHEMATICA

z = 120; a[n_] := Round[1/(Log[(2 n + 1)/(2 n - 1)] - 1/n)]

t = Table[a[n], {n, 1, z}] (* A227513 *)

CROSSREFS

Cf. A227512.

Sequence in context: A015467 A144783 A227512 * A052266 A027325 A228420

Adjacent sequences:  A227510 A227511 A227512 * A227514 A227515 A227516

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 14 2013

STATUS

approved

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Last modified December 9 03:27 EST 2019. Contains 329872 sequences. (Running on oeis4.)