The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A117704

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Least refined sequence that can be grouped to sum to either natural numbers or odd numbers.
(history; published version)

#8 by Charles R Greathouse IV at Sat Jul 13 12:03:23 EDT 2013

LINKS

_Reinhard Zumkeller_, , <a href="/A117704/b117704.txt">Table of n, a(n) for n = 1..10000</a>

Discussion

Sat Jul 13

12:03

OEIS Server: https://oeis.org/edit/global/1934

#7 by N. J. A. Sloane at Fri Feb 22 21:38:08 EST 2013

LINKS

_Reinhard Zumkeller, _, <a href="/A117704/b117704.txt">Table of n, a(n) for n = 1..10000</a>

PROG

-- _Reinhard Zumkeller, _, Aug 03 2011

Discussion

Fri Feb 22

21:38

OEIS Server: https://oeis.org/edit/global/1866

#6 by Russ Cox at Sat Mar 31 13:21:30 EDT 2012

AUTHOR

Frank _Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), _, Apr 27 2006

Discussion

Sat Mar 31

13:21

OEIS Server: https://oeis.org/edit/global/884

#5 by Bruno Berselli at Thu Aug 04 08:53:28 EDT 2011

STATUS

editing

approved

#4 by Bruno Berselli at Thu Aug 04 08:53:24 EDT 2011

KEYWORD

easy,nonn,easy,changed

STATUS

proposed

editing

#3 by Reinhard Zumkeller at Wed Aug 03 16:32:21 EDT 2011

STATUS

editing

proposed

#2 by Reinhard Zumkeller at Wed Aug 03 16:00:02 EDT 2011

LINKS

Reinhard Zumkeller, <a href="/A117704/b117704.txt">Table of n, a(n) for n = 1..10000</a>

PROG

(Haskell)

a117704 n = a117704_list !! (n-1)

a117704_list = 1 : zipWith (-) (tail a005214_list) a005214_list

-- Reinhard Zumkeller, Aug 03 2011

STATUS

approved

editing

#1 by N. J. A. Sloane at Fri May 19 03:00:00 EDT 2006

NAME

Least refined sequence that can be grouped to sum to either natural numbers or odd numbers.

DATA

1, 2, 1, 2, 3, 1, 5, 1, 5, 4, 3, 8, 9, 4, 6, 9, 2, 12, 3, 10, 9, 5, 15, 1, 15, 8, 9, 16, 2, 19, 6, 14, 15, 6, 22, 3, 20, 13, 11, 24, 1, 26, 10, 17, 22, 6, 29, 6, 24, 19, 12, 32, 1, 32, 15, 19, 30, 5, 36, 10, 27, 26, 12, 39, 4, 36, 21, 20, 39, 3, 43, 15, 29, 34, 11, 46, 8, 39, 28, 20, 49, 50

OFFSET

1,2

COMMENTS

In other words, least common refinement of the natural numbers and the odd numbers.

FORMULA

a(n) = A005214(n) - A005214(n-1).

EXAMPLE

As natural numbers: 1,2,1+2,3+1,5,1+5,4+3,8,...

As odd numbers: 1,2+1,2+3,1+5+1,5+4,3+8,...

CROSSREFS

Cf. A118382, A005214, A000027, A005408.

KEYWORD

easy,nonn

AUTHOR

Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 27 2006

STATUS

approved