Search: id:A056753
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%I A056753
%S A056753 1,3,1,5,1,3,1,7,1,3,1,9,1,3,1,7,1,3,1,11,1,3,1,7,1,3,1,13,1,3,1,7,1,3,
%T A056753 1,15,1,3,1,7,1,3,1,17,1,3,1,7,1,3,1,15,1,3,1,7,1,3,1,19,1,3,1,7,1,3,1,
%U A056753 15,1,3,1,7,1,3,1,21,1,3,1,7,1,3,1,15,1,3,1,7,1,3,1,23,1,3,1,7,1,3,1
%N A056753 Only odd numbers occur and for all k there are k numbers between any 
               two successive occurrences of k.
%C A056753 Only the numbers 2^m - 1 occur more than once.
%C A056753 a(A005843(n))=1; a(A016813(n))=3; a(A004771(n))=7; a(A008598(n)+35)=15; 
               a(A008598(n)+155)=31. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Aug 23 2009]
%H A056753 R. Zumkeller, <a href="b056753.txt">Table of n, a(n) for n = 0..10000</
               a> [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 
               23 2009]
%F A056753 Let x=a(n-A164632(n)), a(n) = if (x occured exactly once so far) then 
               x+2 else x. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Aug 23 2009]
%o A056753 Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Aug 23 2009: (Start)
%o A056753 (Other) PolyML (the leading dots are just for readability):
%o A056753 fun A056753(n) =
%o A056753 ... let fun f(i, x, y, z) =
%o A056753 ........... if i = n
%o A056753 ............ then if x = 1
%o A056753 .................. then A056753(n - z) + 2
%o A056753 .................. else A056753(n - z)
%o A056753 ............ else if x = 1
%o A056753 .................. then if y = 1
%o A056753 ........................ then f(i + 1, 2*z, z, 2*z)
%o A056753 ........................ else f(i + 1, z, y - 1, z)
%o A056753 .................. else f(i + 1, x - 1, y, z)
%o A056753 .... in if n = 0
%o A056753 ........ then 1
%o A056753 ........ else f(1, 1, 1, 1)
%o A056753 ... end; (End)
%Y A056753 Sequence in context: A085407 A016475 A037227 this_sequence A154723 A114567 
               A001051
%Y A056753 Adjacent sequences: A056750 A056751 A056752 this_sequence A056754 A056755 
               A056756
%K A056753 nice,nonn
%O A056753 0,2
%A A056753 Claude Lenormand (claude.lenormand(AT)free.fr), Jan 19 2001

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