Search: id:A004956
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%I A004956
%S A004956 0,2,4,5,7,9,10,12,13,15,17,18,20,22,23,25,26,28,30,31,
%T A004956 33,34,36,38,39,41,43,44,46,47,49,51,52,54,56,57,59,60,
%U A004956 62,64,65,67,68,70,72,73,75,77,78,80,81,83,85,86,88,89
%N A004956 Ceiling of n*phi, phi = (1+sqrt(5))/2.
%C A004956 a(0)=0, a(1)=2; for n>1, a(n)=a(n-1)+2 if n is already in the sequence, 
               a(n)=a(n-1)+1 otherwise.
%C A004956 Integer solutions to the equation x=ceiling(phi*floor(x/phi)) - Benoit 
               Cloitre (benoit7848c(AT)orange.fr), Feb 14 2004
%C A004956 Benoit Cloitre, Mar 05 2007: (Start) The following is an alternative 
               way to obtain this sequence. NP means "term not in parentheses". 
               Write down the natural numbers and mark the least NP, which is 1:
%C A004956 1* 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ...
%C A004956 Take the 1st NP (which is 1) and parenthesize it; mark the least NP (which 
               is 2):
%C A004956 (1*) 2* 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ...
%C A004956 Take the 2nd NP (which is 3) and parenthesize it; mark the next NP (which 
               is 4):
%C A004956 (1*) 2* (3) 4* 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ...
%C A004956 Take the 4th NP (which is 6) and parenthesize it; mark the next NP (which 
               is 5):
%C A004956 (1*) 2* (3) 4* 5* (6) 7 8 9 10 11 12 13 14 15 16 17 18 19 ...
%C A004956 Continuing in this way we obtain
%C A004956 (1*) 2* (3) 4* 5* (6) 7* (8) 9* 10* (11) 12* 13* (14) 15* (16) 17* (18) 
               19* ...
%C A004956 The starred entries (after the first) give the sequence. (End)
%H A004956 B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/index.html">Numerical analogues of Aronson's sequence</
               a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
%H A004956 B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://arXiv.org/
               abs/math.NT/0305308">Numerical analogues of Aronson's sequence</a> 
               (math.NT/0305308)
%Y A004956 Essentially same as A026351.
%Y A004956 Sequence in context: A026463 A087063 A047497 this_sequence A026351 A047212 
               A121347
%Y A004956 Adjacent sequences: A004953 A004954 A004955 this_sequence A004957 A004958 
               A004959
%K A004956 nonn,easy
%O A004956 0,2
%A A004956 N. J. A. Sloane (njas(AT)research.att.com).

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