login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007066 a(n) = 1 + ceiling((n-1)*phi^2), phi = (1+sqrt(5))/2.
(Formerly M3299)
14
1, 4, 7, 9, 12, 15, 17, 20, 22, 25, 28, 30, 33, 36, 38, 41, 43, 46, 49, 51, 54, 56, 59, 62, 64, 67, 70, 72, 75, 77, 80, 83, 85, 88, 91, 93, 96, 98, 101, 104, 106, 109, 111, 114, 117, 119, 122, 125, 127, 130, 132, 135, 138, 140, 143, 145, 148, 151, 153, 156, 159, 161, 164, 166 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First column of dual Wythoff array.

Positions of 0 in A189479.

REFERENCES

C. Kimberling, "Stolarsky interspersions," Ars Combinatoria 39 (1995) 129-138.

D. R. Morrison, "A Stolarsky array of Wythoff pairs," in A Collection of Manuscripts Related to the Fibonacci Sequence. Fibonacci Assoc., Santa Clara, CA, 1980, pp. 134-136.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

C. Kimberling, Interspersions

N. J. A. Sloane, Classic Sequences

FORMULA

Floor(1+phi*floor(phi*(n-1)+1)), phi=(1+sqrt(5))/2, n >= 2.

a(1)=1; for n>1, a(n)=a(n-1)+2 if n is already in the sequence, a(n)=a(n-1)+3 otherwise. - Benoit Cloitre, Mar 06 2003

MAPLE

Digits := 100: t := (1+sqrt(5))/2; A007066 := proc(n) if n <= 1 then 1 else floor(1+t*floor(t*(n-1)+1)); fi; end;

MATHEMATICA

t = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0, 1}}] &, {0}, 6] (*A189479*)

Flatten[Position[t, 0]] (*A007066*)

Flatten[Position[t, 1]] (*A099267*)

With[{grs=GoldenRatio^2}, Table[1+Ceiling[grs(n-1)], {n, 70}]] (* Harvey P. Dale, Jun 24 2011 *)

PROG

(Haskell)

a007066 n = a007066_list !! (n-1)

a007066_list = 1 : f 2 [1] where

   f x zs@(z:_) = y : f (x + 1) (y : zs) where

     y = if x `elem` zs then z + 2 else z + 3

-- Reinhard Zumkeller, Sep 26 2014, Sep 18 2011

CROSSREFS

Cf. A064437. Apart from initial terms, same as A026356. Complement is (essentially) A026355. Equals 1 + A004957, also n + A004956.

First differences give A076662.

Complement of A099267. [From Gerald Hillier, Dec 19 2008]

Cf. A193214 (primes).

Sequence in context: A086824 A080574 A189367 * A047537 A247985 A190438

Adjacent sequences:  A007063 A007064 A007065 * A007067 A007068 A007069

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Mira Bernstein

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified November 22 23:43 EST 2014. Contains 249835 sequences.