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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 Upper Wythoff sequence plus 2, when shifted by 1. - Michel Dekking, Aug 26 2019 REFERENCES Clark 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 Clark Kimberling, Interspersions Matthew Skala, Graph Nimors, arXiv preprint arXiv:1604.04072 [math.CO], 2016. N. J. A. Sloane, Classic Sequences FORMULA a(n) = 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 a(n+1) = floor(n*phi^2) + 2, n>=1. - Michel Dekking, Aug 26 2019 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  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 (Python) from math import isqrt def A007066(n): return (n+1+isqrt(5*(n-1)**2)>>1)+n if n > 1 else 1 # Chai Wah Wu, Aug 25 2022 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). Except for the first term equal to A001950 + 2. Sequence in context: A189367 A310951 A310952 * A260395 A047537 A247985 Adjacent sequences:  A007063 A007064 A007065 * A007067 A007068 A007069 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified September 27 19:37 EDT 2022. Contains 357063 sequences. (Running on oeis4.)