A227512 Floor(-1/n + 1/log((2n+1)/(2n-1))).

10, 92, 318, 760, 1490, 2581, 4103, 6129, 8731, 11981, 15952, 20714, 26340, 32902, 40472, 49123, 58925, 69951, 82273, 95963, 111094, 127736, 145962, 165844, 187454, 210865, 236147, 263373, 292615, 323945, 357436, 393158, 431184, 471586, 514436, 559807

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 - floor(9*n/5) - 1. (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 + 72 x^2 + 72 x^3 + 72 x^4 + 63 x^5 + 8 x^6 + x^7)/((-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) = 760.

Mathematica

z = 120; a[n_] := Floor[1/(Log[(2 n + 1)/(2 n - 1)] - 1/n)]; t = Table[a[n], {n, 1, z}]

Crossrefs

Cf. A227513.

Sequence in context: A015467 A144783 A365217 * A227513 A052266 A027325

Adjacent sequences: A227509 A227510 A227511 * A227513 A227514 A227515

Keyword

nonn,easy

Author

Clark Kimberling, Jul 14 2013

Status

approved