(Translated by https://www.hiragana.jp/)
A056753 - OEIS
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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
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
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
KEYWORD
nice,nonn,look
AUTHOR
Claude Lenormand (claude.lenormand(AT)free.fr), Jan 19 2001
STATUS
approved