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A007066 a(n) = 1 + ceiling((n-1)*phi^2), phi = (1+sqrt(5))/2.
(Formerly M3299)
17
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's in A189479.

Skala (2016) asks if this sequence also gives the positions of the 0's in A283310. - N. J. A. Sloane, Mar 06 2017

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

Matthew Skala, Graph Nimors, arXiv preprint arXiv:1604.04072 [math.CO], 2016.

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. [Gerald Hillier, Dec 19 2008]

Cf. A193214 (primes).

Sequence in context: A189367 A310951 A310952 * A260395 A047537 A247985

Adjacent sequences:  A007063 A007064 A007065 * A007067 A007068 A007069

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Mira Bernstein

STATUS

approved

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Last modified December 15 20:10 EST 2018. Contains 318154 sequences. (Running on oeis4.)