|
Search: id:A003622
|
|
|
| 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)
|
|
|
Search completed in 0.003 seconds
|
