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A116941 Permutation of the natural numbers in conjunction with A116939 and A003056.

%I A116941 #21 Oct 08 2017 23:47:18
%S A116941 0,1,3,2,4,6,5,7,9,11,8,10,12,14,16,13,15,17,19,21,23,18,20,22,24,26,
%T A116941 28,30,25,27,29,31,33,35,37,39,32,34,36,38,40,42,44,46,48,41,43,45,47,
%U A116941 49,51,53,55,57,59,50,52,54,56,58,60,62,64,66,68,70,61,63,65,67,69,71,73
%N A116941 Permutation of the natural numbers in conjunction with A116939 and A003056.
%C A116941 Inverse: A116942;
%C A116941 A003056(n) = A116939(a(n)).
%H A116941 Reinhard Zumkeller, <a href="/A116941/b116941.txt">Table of n, a(n) for n = 0..10000</a>
%H A116941 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A116941 a(n) = A074147(n+1) - 1. - _Robert G. Wilson v_, Mar 09 2017
%t A116941 Table[ Ceiling[(n -1)^2/2] + 2k -2, {n, 12}, {k, n}] // Flatten (* _Robert G. Wilson v_, Mar 09 2017 after _Ivan Neretin_ in A074147 *)
%o A116941 (Haskell)
%o A116941 a116941 n = a116941_list !! n
%o A116941 a116941_list = f 0 1 (zip a116939_list [0..]) [] where
%o A116941    f u v xis'@((x,i):xis) ws
%o A116941      | x == u    = i : f u v xis ws
%o A116941      | x == v    = f u v xis (i : ws)
%o A116941      | otherwise = reverse ws ++ f v x xis' []
%o A116941 -- _Reinhard Zumkeller_, Jun 28 2013
%K A116941 nonn
%O A116941 0,3
%A A116941 _Reinhard Zumkeller_, Feb 27 2006