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A056535 Mapping from the ordering by sum to the ordering by product of the ordered pairs. Inverse permutation to A056534.

%I A056535 #18 Oct 15 2015 12:23:09
%S A056535 1,2,3,4,7,5,6,12,13,8,9,18,22,19,10,11,25,32,33,26,14,15,31,43,48,44,
%T A056535 34,16,17,39,55,63,64,56,40,20,21,47,68,80,86,81,69,49,23,24,54,79,98,
%U A056535 107,108,99,82,57,27,28,62,93,116,129,136,130,117,94,65,29,30,72,106
%N A056535 Mapping from the ordering by sum to the ordering by product of the ordered pairs. Inverse permutation to A056534.
%C A056535 The last term of the each row r of the triangle is the first term of that row + (tau(r)-1).
%C A056535 As an array, T(n,k) is the index of the k-th term of A027750 whose value is n. - _Michel Marcus_, Oct 15 2015
%H A056535 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A056535 [seq(nthmember(j, A056534), j=1..105)];
%e A056535 As a triangle, sequence begins:
%e A056535 1;
%e A056535 2, 3;
%e A056535 4, 7, 5;
%e A056535 6, 12, 13, 8;
%e A056535 9, 18, 22, 19, 10;
%e A056535 ...
%e A056535 As an array, sequence begins:
%e A056535 1,   2,  4,  6,  9,  11,  15, ...
%e A056535 3,   7, 12, 18, 25,  31,  39, ...
%e A056535 5,  13, 22, 32, 43,  55,  68, ...
%e A056535 8,  19, 33, 48, 63,  80,  98, ...
%e A056535 10, 26, 44, 64, 86, 107, 129, ...
%e A056535 ...
%p A056535 Maple procedure nthmember given in A054426.
%t A056535 a[n_] := If[p = Position[A056534, n]; p != {}, p[[1, 1]], 0]; (* _Jean-François Alcover_, Aug 20 2013 *)
%Y A056535 A056535[A000217[i]] = A056535[A000217[i-1]+1]+A000005[i]-1, for all i >= 1.
%Y A056535 Left edge: A054519, Right edge: A006218.
%K A056535 nonn,tabl
%O A056535 1,2
%A A056535 _Antti Karttunen_, Jun 20 2000