

A227512


Floor(1/n + 1/log((2n+1)/(2n1))).


2



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
(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  floor(9*n/5)  1. (conjectured, based on computations by Peter J. C. Moses, Jul 14 2013)
a(n) = 3*a(n1)  3*a(n2) + a(n3) + a(n5)  3*a(n6) + 3*a(n7)  a(n8) (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: A267833 A015467 A144783 * A227513 A052266 A027325
Adjacent sequences: A227509 A227510 A227511 * A227513 A227514 A227515


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jul 14 2013


STATUS

approved



