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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
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
Sequence in context: A213741 A184825 A190372 * A197120 A319449 A030374
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 23 2011
STATUS
approved

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Last modified July 16 08:10 EDT 2024. Contains 374345 sequences. (Running on oeis4.)