A056753 Only odd numbers occur and for all k there are k numbers between any two successive occurrences of k.

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

Offset

0,2

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. - Reinhard Zumkeller, Aug 23 2009

A181497(n) = smallest m such that A056753(m) = 2*n + 1. - Reinhard Zumkeller, Oct 24 2010

Links

R. Zumkeller, Table of n, a(n) for n = 0..10000

Formula

Let x = a(n - A164632(n)), a(n) = if (x occured exactly once so far) then x+2 else x. - Reinhard Zumkeller, Aug 23 2009

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}] (* Jean-François Alcover, Dec 14 2011, after Reinhard Zumkeller *)

Prog

(PolyML)
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;
(* Reinhard Zumkeller, Feb 25 2012, Aug 23 2009 *)
(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; // Klaus Brockhaus, Oct 25 2010
(Haskell)
import Data.List (intercalate, group)
a056753 n = a056753_list !! n
a056753_list = [1] ++ odds [] where
   odds xs = xs ++ (intercalate xs' $ group [y+2, y+4..2*y+1]) ++ odds xs'
        where y = 2 * length xs + 1
              xs' = xs ++ [y] ++ xs
-- Reinhard Zumkeller, Feb 25 2012, Oct 24 2010

Crossrefs

Sequence in context: A352483 A016475 A037227 * A243158 A154723 A273262

Adjacent sequences: A056750 A056751 A056752 * A056754 A056755 A056756

Keyword

nice,nonn,look

Author

Claude Lenormand (claude.lenormand(AT)free.fr), Jan 19 2001

Status

approved