A056054 a(n) = smallest even number 2m such that value of odd harmonic series Sum_{j=0..m} 1/(2j) is > n.

8, 62, 454, 3348, 24734, 182760, 1350428, 9978382, 73730824, 544801200, 4025566630, 29745137662, 219788490858, 1624029488844, 12000044999386, 88669005690160, 655180257281000, 4841163675961122, 35771629985782052

Offset

1,1

Comments

Numbers 2*m such that floor(f(m))=floor(f(m-1)) where f(m)= Sum_{j=1..m} ((2*j-1)/(2*j)). Examples: floor(f(1))=floor(1/2)=0; floor(f(2))=floor(1/2+2/3)=floor(1,25)=1, then 2*2=4 is not in the sequence; floor(f(3))=floor((1/2+3/4+4/5)=floor(2,083..)=2, then 2*3=6 is not in the sequence; floor((f(4))=floor(1/2+3/4+5/6+7/8)=floor(2,958..)=2, then 2*4=8 is the first term of the sequence. - Philippe Lallouet (philip.lallouet(AT)wanadoo.fr), Aug 15 2007

References

Calvin C. Clawson, Mathematical Mysteries, The Beauty and Magic of Numbers, Plenum Press, NY and London, 1996, page 64.

Links

Table of n, a(n) for n=1..19.

Formula

a(n) = 2*A002387(2n).

The next term is approximately the previous term * e^2.

Mathematica

s = 0; k = 2; Do[ While[s = N[s + 1/k, 24]; s <= n, k += 2]; Print[k]; k += 2, {n, 1, 12}]
(* or assuming that the Mathematica coding in A002387 is correct then *)
b[n_] := Module[{k = Floor[2a[2n]]}, If[ EvenQ[k], k, k + 1]]; Table[ b[n], {n, 19}] (* Robert G. Wilson v, Apr 17 2004 *)

Crossrefs

Cf. A002387, A056053, A091463, A091464, A091465.

Cf. A056054.

Sequence in context: A269607 A296584 A198690 * A167251 A227439 A144143

Adjacent sequences: A056051 A056052 A056053 * A056055 A056056 A056057

Keyword

nonn

Author

Robert G. Wilson v, Jul 25 2000 and Jan 11 2004

Status

approved