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A007066
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a(n) = 1 + ceiling((n-1)*phi^2), phi = (1+sqrt(5))/2.
(Formerly M3299)
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14
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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
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OFFSET
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1,2
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COMMENTS
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First column of dual Wythoff array.
Positions of 0 in A189479.
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REFERENCES
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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).
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..10000
C. Kimberling, Interspersions
N. J. A. Sloane, Classic Sequences
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FORMULA
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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.
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MAPLE
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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;
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MATHEMATICA
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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}]] (* From Harvey P. Dale, June 24 2011 *)
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PROG
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(Haskell)
a007066 n = a007066_list !! (n-1)
a007066_list = f 1 [1..] 0 where
f k xs y = g : f (k+1) (ys ++ xs') g where
(ys, _:xs') = span (< g) xs
g = xs !! (xs !! (k-1) - 1)
-- Reinhard Zumkeller, Sep 18 2011
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CROSSREFS
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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 A190438 A189526
Adjacent sequences: A007063 A007064 A007065 * A007067 A007068 A007069
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane, Mira Bernstein (mira(AT)math.berkeley.edu)
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STATUS
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approved
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