%I A060143
%S A060143 0,0,1,1,2,3,3,4,4,5,6,6,7,8,8,9,9,10,11,11,12,12,13,14,14,15,16,16,17,
%T A060143 17,18,19,19,20,21,21,22,22,23,24,24,25,25,26,27,27,28,29,29,30,30,31,
%U A060143 32,32,33,33,34,35,35,36,37,37,38,38,39,40,40,41,42,42,43,43,44,45,45
%N A060143 Floor(n/tau).
%C A060143 Fibonacci base shift right: a(n) = Sum_{k in A_n} F_{k-1}, where a(n)= 
               Sum_{k in A_n} F_k (unique) expression of n as a sum of ``noncontiguous'' 
               Fibonacci numbers (with index >=2). - Michele Dondi (bik.mido(AT)tiscalenet.it), 
               Dec 30, 2001
%C A060143 Numerators a(n) of fractions slowly converging to phi, the golden ratio: 
               let a(1) = 0, b(n) = n - a(n); if (a(n) + 1) / b(n) < (1 + sqrt(5))/
               2, then a(n+1) = a(n) + 1, else a(n+1)= a(n). a(n) + b(n) = n and 
               as n -> +infinity, a(n) / b(n) converges to (1 + sqrt(5))/2. For 
               all n, a(n) / b(n) < (1 + sqrt(5))/2. a(1) = 0. b(n) = n - a(n). 
               If (a(n) + 1) / b(n) < sqrt(3), then a(n+1) = a(n) + 1, else a(n+1) 
               = a(n). - Robert A. Stump (bee_ess107(AT)msn.com), Sep 22 2002
%C A060143 a(10^n) gives the first few digits of phi=(sqrt(5)-1)/2.
%C A060143 a(n)=a(n+1) iff n in A066096.
%H A060143 Harry J. Smith, <a href="b060143.txt">Table of n, a(n) for n=0,...,1000</
               a>
%F A060143 a(n)=floor(phi(n)), where phi=(sqrt(5)-1)/2. [Corrected by Casey Mongoven 
               (cm(AT)caseymongoven.com), Jul 18 2008]
%F A060143 a(F_n)=F_{n-1} if F_n is the N_th Fibonacci number.
%F A060143 A006336(n) = A006336(n-1) + A006336(a(n)) for n>1. - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Oct 24 2007
%F A060143 a(n) = floor(n*phi) - n, where phi = (1+sqrt(5))/2. - William A. Tedeschi 
               (fynmun(AT)hotmail.com), Mar 06 2008
%e A060143 a(6)= 3 so b(6) = 6 - 3 = 3. a(7) = 4 because (a(6) + 1) / b(6) = 4/3 
               which is < (1 + sqrt(5))/2. So b(7) = 7 - 4 = 3. a(8) = 4 because 
               (a(7) + 1) / b(7) = 5/3 which is > (1 + sqrt(5))/2.
%o A060143 (PARI) { default(realprecision, 10); p=(sqrt(5) - 1)/2; for (n=0, 1000, 
               write("b060143.txt", n, " ", floor(n*p)); ) } [From Harry J. Smith 
               (hjsmithh(AT)sbcglobal.net), Jul 02 2009]
%Y A060143 Cf. A074840, A074065, A035336, A022342, A066094-A066096.
%Y A060143 Apart from initial terms, same as A005206.
%Y A060143 Sequence in context: A090638 A057363 A073869 this_sequence A005206 A057365 
               A014245
%Y A060143 Adjacent sequences: A060140 A060141 A060142 this_sequence A060144 A060145 
               A060146
%K A060143 easy,frac,nonn
%O A060143 0,5
%A A060143 Clark Kimberling (ck6(AT)evansville.edu), Mar 05 2001
%E A060143 I merged three identical sequences to create this entry. Some of the 
               formulae may need their initial terms adjusting now. - N. J. A. Sloane 
               (njas(AT)research.att.com), Mar 05 2003
%E A060143 More terms from William A. Tedeschi (fynmun(AT)hotmail.com), Mar 06 2008