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A184835 a(n) = n + floor(n/t) + floor(n/t^2) + floor(n/t^3) + floor(n/t^4), where t is the pentanacci constant. 7
1, 3, 4, 7, 8, 10, 11, 15, 16, 18, 19, 22, 23, 25, 27, 31, 32, 34, 35, 38, 39, 41, 43, 46, 47, 49, 50, 53, 54, 57, 60, 62, 63, 65, 67, 69, 70, 73, 75, 77, 78, 80, 82, 84, 86, 89, 91, 93, 94, 96, 98, 100, 101, 104, 106, 108, 109, 112, 114, 116, 119, 121, 123, 124, 126, 128, 130, 131, 134, 136, 138, 139, 141, 143, 146, 148, 150, 152, 154, 155, 157, 159, 161, 163, 165, 167, 169, 170, 173, 175, 177, 179, 182, 183, 185, 186, 189, 190, 193, 194, 197, 198, 200, 201, 205, 206, 209, 210, 213, 214, 216, 217, 220, 222, 224, 227, 228 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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..117.

FORMULA

Limit a(n)/n = t = 1.9659482366454853371899373...

a(n) = n + floor(n*p/u) + floor(n*q/u) + floor(n*r/u) + floor(n*s/u), 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 = 1 + 1/t + 1/t^2 + 1/t^3 + 1/t^4,

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

MATHEMATICA

With[{pc=x/.FindRoot[x^5-x^4-x^3-x^2-x-1==0, {x, 1.96}, WorkingPrecision-> 100]}, Table[n+Total[Table[Floor[n/pc^i], {i, 4}]], {n, 150}]] (* Harvey P. Dale, Jun 21 2011 *)

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^4)}

CROSSREFS

Cf. A184836, A184837, A184838, A184839; A184820, A184823, A184812, A103814.

Sequence in context: A219897 A047344 A005187 * A184823 A242921 A091934

Adjacent sequences:  A184832 A184833 A184834 * A184836 A184837 A184838

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 23 2011

STATUS

approved

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Last modified October 1 15:55 EDT 2020. Contains 337443 sequences. (Running on oeis4.)