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Least refined sequence that can be grouped to sum to either natural numbers or odd numbers.
2

%I #8 Jul 13 2013 12:03:23

%S 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,

%T 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,

%U 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

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

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

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

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

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

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

%o (Haskell)

%o a117704 n = a117704_list !! (n-1)

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

%o -- _Reinhard Zumkeller_, Aug 03 2011

%Y Cf. A118382, A005214, A000027, A005408.

%K nonn,easy

%O 1,2

%A _Franklin T. Adams-Watters_, Apr 27 2006