

A126759


a(0) = 1; a(2n) = a(n); a(3n) = a(n); otherwise write n = 6i+j, where j = 1 or 5 and set a(n) = 2i+2 if j = 1, otherwise a(n) = 2i+3.


4



1, 2, 2, 2, 2, 3, 2, 4, 2, 2, 3, 5, 2, 6, 4, 3, 2, 7, 2, 8, 3, 4, 5, 9, 2, 10, 6, 2, 4, 11, 3, 12, 2, 5, 7, 13, 2, 14, 8, 6, 3, 15, 4, 16, 5, 3, 9, 17, 2, 18, 10, 7, 6, 19, 2, 20, 4, 8, 11, 21, 3, 22, 12, 4, 2, 23, 5, 24, 7, 9, 13, 25, 2, 26, 14, 10, 8, 27, 6, 28, 3, 2, 15, 29, 4, 30, 16, 11, 5, 31, 3
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OFFSET

0,2


COMMENTS

Invented by Miles Okazaki, who said: I was trying to write a composition that has the same melody going at several different speeds. If this sequence is mapped onto musical notes and you play every other term, you get the original sequence at half speed. If you play every third term, you again get the same melody. And every 4th term, 6th term, 8th term, 12th term, etc. yields the same result. The pattern generates itself, adding two new increasing integers every six terms.
The formula in the definition encapsulates this verbal description  N. J. A. Sloane.
For k>1: a(A007310(k1))=k and a(m)<k for m < A007310(k1).  Reinhard Zumkeller, Jun 16 2008
For n > 0: a(A007310(n)) = n and a(m) < n for m < A007310(n).  Reinhard Zumkeller, May 23 2013


LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..10000


FORMULA

a(0) = 1, a(2n) = a(n), a(3n) = a(n), a(6n+1) = 2n + 2, a(6n1) = 2n + 1. [Essentially same as the original description, except the last clause expressed slightly differently.]  Antti Karttunen, Jan 28 2015


MAPLE

a:=proc(n) option remember; local i, j;
if n = 0 then RETURN(1); fi;
if n mod 2 = 0 then RETURN(a(n/2)); fi;
if n mod 3 = 0 then RETURN(a(n/3)); fi;
j := n mod 6; i := (nj)/6;
if j = 1 then RETURN(2*i+2) else RETURN(2*i+3); fi;
end;
[seq(a(n), n=0..100)];


MATHEMATICA

a[n_] := a[n] = Module[{i, j}, If[n == 0, Return[1]]; If[Mod[n, 2] == 0, Return[a[n/2]]]; If[Mod[n, 3] == 0, Return[a[n/3]]]; j = Mod[n, 6]; i = (nj)/6; If[j == 1, Return[2*i+2], Return[2*i+3]]]; Table[a[n], {n, 0, 90}] (* JeanFrançois Alcover, Feb 11 2014, after Maple *)


PROG

(Haskell)
a126759 n = a126759_list !! n
a126759_list = 1 : f 1 where
f n = (case mod n 6 of 1 > 2 * div n 6 + 2
5 > 2 * div n 6 + 3
3 > a126759 $ div n 3
_ > a126759 $ div n 2) : f (n + 1)
 Reinhard Zumkeller, May 23 2013
(Scheme)
(definec (A126759 n) (cond ((zero? n) 1) ((even? n) (A126759 (/ n 2))) ((zero? (modulo n 3)) (A126759 (/ n 3))) ((= 1 (modulo n 6)) (+ 2 (/ ( n 1) 3))) (else (+ 1 (/ (+ n 1) 3)))))
;; Antti Karttunen, Jan 28 2015


CROSSREFS

One more than A126760.
Cf. A007310.
Sequence in context: A088019 A301508 A178930 * A293444 A302791 A305979
Adjacent sequences: A126756 A126757 A126758 * A126760 A126761 A126762


KEYWORD

nonn,nice,hear


AUTHOR

N. J. A. Sloane, based on email from Miles Okazaki (milesokazaki(AT)gmail.com), Feb 18 2007


EXTENSIONS

Typo in definition corrected by Reinhard Zumkeller, Jun 16 2008


STATUS

approved



