login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A184837 a(n) = n + floor(n*t) + floor(n*t^2) + floor(n/t) + floor(n/t^2), where t is the pentanacci constant. 5
5, 13, 20, 29, 36, 44, 51, 59, 66, 74, 81, 90, 97, 105, 111, 120, 127, 135, 142, 151, 158, 166, 172, 181, 188, 196, 203, 212, 219, 225, 233, 241, 248, 256, 264, 272, 279, 286, 294, 302, 309, 317, 325, 333, 339, 347, 355, 363, 370, 378, 386, 393, 400, 408, 416, 424, 431, 440, 447, 453, 461, 469, 477, 484, 492, 500, 507, 514, 522, 530, 538, 545, 553, 561, 568, 575, 583, 591, 599, 606, 614, 621, 629, 636, 644, 652, 660, 667, 674, 681, 689, 696, 705, 712, 720, 727, 735, 742, 750, 757, 766, 773, 781, 787, 796, 803 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is one of five sequences that partition the positive integers.

Given t is the pentanacci constant, then the following sequences are disjoint:

. A184835(n) = n + [n/t] + [n/t^2] + [n/t^3] + [n/t^4],

. A184836(n) = n + [n*t] + [n/t] + [n/t^2] + [n/t^3],

. A184837(n) = n + [n*t] + [n*t^2] + [n/t] + [n/t^2],

. A184838(n) = n + [n*t] + [n*t^2] + [n*t^3] + [n/t],

. A184839(n) = n + [n*t] + [n*t^2] + [n*t^3] + [n*t^4], where []=floor.

This is a special case of Clark Kimberling's results given in A184812.

LINKS

Table of n, a(n) for n=1..106.

FORMULA

Limit a(n)/n = t^3 = 7.5982964914823797216620775...

a(n) = n + floor(n*p/r) + floor(n*q/r) + floor(n*s/r) + floor(n*u/r), where p=t, q=t^2, r=t^3, s=t^4, u=t^5, and t is the pentanacci constant.

EXAMPLE

Given t = pentanacci constant, then t^3 = 1 + t + t^2 + 1/t + 1/t^2,

t = 1.965948236645..., t^2 = 3.864952469169..., t^3 = 7.598296491482..., t^4 = 14.93785758893..., t^5 = 29.36705478623...

PROG

(PARI) {a(n)=local(t=real(polroots(1+x+x^2+x^3+x^4-x^5)[1])); n+floor(n*t)+floor(n*t^2)+floor(n/t)+floor(n/t^2)}

CROSSREFS

Cf. A184835, A184836, A184838, A184839; A184812, A103814.

Sequence in context: A213741 A184825 A190372 * A197120 A319449 A030374

Adjacent sequences:  A184834 A184835 A184836 * A184838 A184839 A184840

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 23 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 18 16:27 EST 2020. Contains 331011 sequences. (Running on oeis4.)