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A184838 a(n) = n + floor(n*t) + floor(n*t^2) + floor(n*t^3) + floor(n/t), where t is the pentanacci constant. 5
12, 28, 42, 58, 72, 88, 103, 117, 132, 147, 162, 178, 192, 208, 221, 237, 252, 267, 282, 297, 312, 328, 341, 357, 371, 387, 402, 417, 432, 445, 460, 476, 490, 506, 520, 536, 551, 565, 580, 595, 610, 626, 640, 656, 669, 685, 700, 715, 730, 745, 760, 775, 789, 805, 819, 835, 850, 865, 880, 893, 909, 924, 939, 954, 969, 984, 999, 1013, 1029, 1043, 1059, 1074, 1089, 1104, 1118, 1133, 1149, 1163, 1179, 1193, 1209, 1223, 1238, 1253, 1268, 1283, 1299, 1313, 1327, 1341, 1357, 1372, 1387, 1402, 1417, 1432, 1447 (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^4 = 14.937857588939362411757354...
a(n) = n + floor(n*p/q) + floor(n*r/q) + floor(n*s/q) + floor(n*u/q), 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^4 = 1 + t + t^2 + t^3 + 1/t,
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^3)+floor(n/t)}
CROSSREFS
Sequence in context: A224613 A134618 A108405 * A044073 A044454 A098502
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 23 2011
STATUS
approved

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Last modified June 25 02:10 EDT 2024. Contains 373691 sequences. (Running on oeis4.)