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A056753 Only odd numbers occur and for all k there are k numbers between any two successive occurrences of k. 6
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; text; internal format)
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-Fran├žois 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: A325523 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

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)