Search: id:A003622
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%I A003622 M3278
%S A003622 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,
%T A003622 67,69,72,74,77,80,82,85,88,90,93,95,98,101,103,106,108,111,114,116,119,
%U A003622 122,124,127,129,132,135,137,140,142,145,148,150,153,156,158,161,163,166
%N A003622 [n*phi^2] - 1, phi = (1+sqrt(5))/2.
%C A003622 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.
%C A003622 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
%D A003622 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003622 A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci 
               Association, San Jose, CA, 1972, p. 62.
%D A003622 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, 
               Reading, MA, 1990, p. 307-308 of 2nd edition.
%D A003622 C. Kimberling, "Stolarsky interspersions," Ars Combinatoria 39 (1995) 
               129-138.
%D A003622 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.
%D A003622 J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 10.
%D A003622 N. J. A. Sloane and S. Plouffe, Encyclopedia of Integer Sequences, Academic 
               Press, 1995: this sequence appears twice, as both M3277 and M3278.
%H A003622 T. D. Noe, <a href="b003622.txt">Table of n, a(n) for n=1..1000</a>
%H A003622 C. Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/intersp.html">
               Interspersions</a>
%H A003622 N. J. A. Sloane, <a href="classic.html#WYTH">Classic Sequences</a>
%F A003622 a(n) = [(n+1)*phi] + n; a(n) = [[n*phi]*phi].
%F A003622 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
%F A003622 a(n) = A001950(n) - 1 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), 
               Apr 30 2004
%F A003622 a(n) = A022342(n) + n . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), 
               May 03 2004
%F A003622 a(n)=A(A(n))), n>=1, with A(n):=A000201(n). Wythoff AA-numbers.
%o A003622 (PARI) a(n)=floor(n*(sqrt(5)+3)/2)-1
%Y A003622 a(n)=A022342^2(n)+1.
%Y A003622 Cf. A003623, A022342, A000201. Positions of 1's in A003849.
%Y A003622 Cf. A035336, A022342, A066094-A066097.
%Y A003622 Sequence in context: A003259 A020935 A066095 this_sequence A007073 A047408 
               A060644
%Y A003622 Adjacent sequences: A003619 A003620 A003621 this_sequence A003623 A003624 
               A003625
%K A003622 nonn,easy,nice
%O A003622 1,2
%A A003622 N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Marc LeBrun 
               (mlb(AT)well.com)

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