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Search: id:A003622
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| A003622 |
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[n*phi^2] - 1, phi = (1+sqrt(5))/2.
(Formerly M3278)
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+0
31
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| 1, 4, 6, 9, 12, 14, 17, 19, 22, 25, 27, 30, 33, 35, 38, 40, 43, 46, 48, 51, 53, 56, 59, 61, 64, 67, 69, 72, 74, 77, 80, 82, 85, 88, 90, 93, 95, 98, 101, 103, 106, 108, 111, 114, 116, 119, 122, 124, 127, 129, 132, 135, 137, 140, 142, 145, 148, 150, 153, 156, 158, 161, 163, 166
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also, integers with "odd" Zeckendorf expansions (end with ...+F1 = ...+1) (Fibonacci-odd numbers); first column of Wythoff array A035513; from a 3-way splitting of positive integers.
Also, numbers n such that A005206(n)=A005206(n+1). Also n such that A022342(A005206(n))=n+1 (for all other n's this is n). - Michele Dondi (bik.mido(AT)tiscalenet.it), Dec 30, 2001
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 62.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 307-308 of 2nd edition.
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.
J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 10.
N. J. A. Sloane and S. Plouffe, Encyclopedia of Integer Sequences, Academic Press, 1995: this sequence appears twice, as both M3277 and M3278.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
C. Kimberling, Interspersions
N. J. A. Sloane, Classic Sequences
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FORMULA
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a(n) = [(n+1)*phi] + n; a(n) = [[n*phi]*phi].
G.f.: 1 - (1-x)*sum_{n=1..inf} x^a(n) = 1/1 + x/1 + x^2/1 + x^3/1 + x^5/1 + x^8/1 +...+ x^F(n)/1 +... (continued fraction where F(n)=n-th Fibonacci number). - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 16 2002
a(n) = A001950(n) - 1 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Apr 30 2004
a(n) = A022342(n) + n . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), May 03 2004
a(n)=A(A(n))), n>=1, with A(n):=A000201(n). Wythoff AA-numbers.
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PROGRAM
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(PARI) a(n)=floor(n*(sqrt(5)+3)/2)-1
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CROSSREFS
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a(n)=A022342^2(n)+1.
Cf. A003623, A022342, A000201. Positions of 1's in A003849.
Cf. A035336, A022342, A066094-A066097.
Adjacent sequences: A003619 A003620 A003621 this_sequence A003623 A003624 A003625
Sequence in context: A003259 A020935 A066095 this_sequence A007073 A047408 A060644
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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 (njas(AT)research.att.com), Mira Bernstein, Marc LeBrun (mlb(AT)well.com)
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