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A003622 [n*phi^2] - 1, phi = (1+sqrt(5))/2.
(Formerly M3278)
+0
29
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)
OFFSET

1,2

COMMENT

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

REFERENCES

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.

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

C. Kimberling, Interspersions

N. J. A. Sloane, Classic Sequences

FORMULA

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.

PROGRAM

(PARI) a(n)=floor(n*(sqrt(5)+3)/2)-1

CROSSREFS

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

KEYWORD

nonn,easy,nice

AUTHOR

njas, Mira Bernstein, Marc LeBrun (mlb(AT)well.com)

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Last modified May 15 13:16 EDT 2008. Contains 139641 sequences.


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