Search: id:A126759
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%I A126759
%S A126759 1,2,2,2,2,3,2,4,2,2,3,5,2,6,4,3,2,7,2,8,3,4,5,9,2,10,6,2,4,11,3,12,2,
               5,
%T A126759 7,13,2,14,8,6,3,15,4,16,5,3,9,17,2,18,10,7,6,19,2,20,4,8,11,21,3,22,12,
%U A126759 4,2,23,5,24,7,9,13,25,2,26,14,10,8,27,6,28,3,2,15,29,4,30,16,11,5,31,
               3
%N A126759 a(0) = 1; a(2n) = a(n); a(3n) = a(n); otherwise write n = 6i+j, where 
               j = 1 or 5 and set a(n) = 2i+2 if j = 1, otherwise a(n) = 2i+3.
%C A126759 Invented by Miles Okazaki, who said: I was trying to write a composition 
               that has the same melody going at several different speeds. If this 
               sequence is mapped onto musical notes and you play every other term, 
               you get the original sequence at half speed. If you play every third 
               term, you again get the same melody. And every 4th term, 6th term, 
               8th term, 12-th term, etc. yields the same result. The pattern generates 
               itself, adding two new increasing integers every six terms.
%C A126759 The formula in the definition encapsulates this verbal description - 
               N. J. A. Sloane (njas(AT)research.att.com).
%C A126759 For k>1: a(A007310(k-1))=k and a(m)<k for m<A007310(k-1). - Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 16 2008
%H A126759 N. J. A. Sloane, <a href="b126759.txt">Table of n, a(n) for n = 0..10000</
               a>
%p A126759 a:=proc(n) option remember; local i,j;
%p A126759 if n = 0 then RETURN(1); fi;
%p A126759 if n mod 2 = 0 then RETURN(a(n/2)); fi;
%p A126759 if n mod 3 = 0 then RETURN(a(n/3)); fi;
%p A126759 j := n mod 6; i := (n-j)/6;
%p A126759 if j = 1 then RETURN(2*i+2) else RETURN(2*i+3); fi;
%p A126759 end;
%p A126759 [seq(a(n),n=0..100)];
%Y A126759 Cf. A126760.
%Y A126759 Sequence in context: A147981 A051888 A088019 this_sequence A029348 A070093 
               A058744
%Y A126759 Adjacent sequences: A126756 A126757 A126758 this_sequence A126760 A126761 
               A126762
%K A126759 nonn,nice
%O A126759 0,2
%A A126759 N. J. A. Sloane (njas(AT)research.att.com), based on email from Miles 
               Okazaki (milesokazaki(AT)gmail.com), Feb 18 2007
%E A126759 Typo in definition corrected by Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jun 16 2008

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