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A056753
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Only odd numbers occur and for all k there are k numbers between any two successive occurrences of k.
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6
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Only the numbers 2^m - 1 occur more than once.
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]
A181497(n) = smallest m such that A056753(m) = 2*n + 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 24 2010]
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 0..10000 [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 23 2009]
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FORMULA
| 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]
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MATHEMATICA
| a[n_] := a[n] = (ClearAll[f]; f[i_, x_, y_, z_] := f[i, x, y, z] = If[i == n, If[x == 1, a[n-z] + 2, a[n-z]], If[x == 1, If[y == 1, f[i+1, 2z, z, 2z], f[i+1, z, y-1, z]], f[i+1, x-1, y, z]]]; If[n == 0, 1, f[1, 1, 1, 1]]); Table[a[n], {n, 0, 98}] (* From Jean-François Alcover, Dec 14 2011, after Reinhard Zumkeller *)
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PROG
| Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 23 2009: (Start)
(Other) PolyML (the leading dots are just for readability):
fun A056753(n) =
... let fun f(i, x, y, z) =
........... if i = n
............ then if x = 1
.................. then A056753(n - z) + 2
.................. else A056753(n - z)
............ else if x = 1
.................. then if y = 1
........................ then f(i + 1, 2*z, z, 2*z)
........................ else f(i + 1, z, y - 1, z)
.................. else f(i + 1, x - 1, y, z)
.... in if n = 0
........ then 1
........ else f(1, 1, 1, 1)
... end; (End)
(MAGMA) S:=[ 0: n in [1..100] ]; k:=1; p:=Position(S, 0, 1); while p gt 0 do for j in [p..#S by k+1] do if S[j] eq 0 then S[j]:=k; else break; end if; end for; f:=p; p:=Position(S, 0, f); k+:=2; end while; S; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 25 2010]
Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 24 2010: (Start)
(Other) Haskell
import Data.List (intercalate)
odds :: Integral a => [a] -> [a]
odds xs = xs ++ (intercalate xs' $ map (\x -> [x]) [n+2, n+4..2*n+1])
......... ++ odds xs'
......... where n = fromIntegral $ 2 * length xs + 1
............... xs' = xs ++ [n] ++ xs
a056753_list = [1] ++ odds [] :: [Integer]
-- eop. (End)
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CROSSREFS
| Sequence in context: A085407 A016475 A037227 * A154723 A114567 A001051
Adjacent sequences: A056750 A056751 A056752 * A056754 A056755 A056756
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KEYWORD
| nice,nonn
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AUTHOR
| Claude Lenormand (claude.lenormand(AT)free.fr), Jan 19 2001
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