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A182631 Tetrahedron in which T(i,j,k) is the next number congruent to k mod j of the level j in the slice i, with 0 <= i, 1 <= j, 0 <= k < j.

%I A182631 #18 Feb 06 2023 12:47:54
%S A182631 0,1,0,1,2,2,3,0,1,2,3,4,5,3,4,5,0,1,2,3,4,6,7,6,7,8,4,5,6,7,0,1,2,3,
%T A182631 4,5,8,9,9,10,11,8,9,10,11,5,6,7,8,9,0,1,2,3,4,5,6,10,11,12,13,14,12,
%U A182631 13,14,15,10,11,12,13,14,6,7,8,9,10,11,0,1,2,3,4,5,6
%N A182631 Tetrahedron in which T(i,j,k) is the next number congruent to k mod j of the level j in the slice i, with 0 <= i, 1 <= j, 0 <= k < j.
%e A182631 Tetrahedron begins:
%e A182631 For i=0, j=1, k=0, T(0,1,0)=0 represents the first vertex of the tetrahedron.
%e A182631 For i=1, slice 1 lists the terms
%e A182631   1;
%e A182631   0, 1.
%e A182631 For i=2, slice 2 lists the terms
%e A182631   2;
%e A182631   2, 3;
%e A182631   0, 1, 2.
%e A182631 For i=3, slice 3 lists the terms
%e A182631   3;
%e A182631   4, 5;
%e A182631   3, 4, 5;
%e A182631   0, 1, 2, 3.
%e A182631 For i=4, slice 4 lists the terms
%e A182631   4;
%e A182631   6, 7;
%e A182631   6, 7, 8;
%e A182631   4, 5, 6, 7;
%e A182631   0, 1, 2, 3, 4.
%e A182631 For i=5, slice 5 lists the terms
%e A182631   5;
%e A182631   8,  9;
%e A182631   9, 10, 11;
%e A182631   8,  9, 10, 11;
%e A182631   5,  6,  7,  8,  9;
%e A182631   0,  1,  2,  3,  4,  5.
%e A182631 And so on.
%e A182631 If the sequence is written as a triangle, it begins:
%e A182631   0,
%e A182631   1, 0, 1,
%e A182631   2, 2, 3, 0, 1, 2,
%e A182631   3, 4, 5, 3, 4, 5, 0, 1, 2, 3,
%e A182631   4, 6, 7, 6, 7, 8, 4, 5, 6, 7, 0, 1, 2, 3, 4;
%e A182631   ...
%Y A182631 Cf. A144626.
%Y A182631 Level j=1 column k=0 of tetrahedron = column 1 of triangle gives A001477.
%Y A182631 Level j=2 column k=0 of tetrahedron = column 2 of triangle gives A005843.
%Y A182631 Level j=2 column k=1 of tetrahedron = column 3 of triangle gives A005408.
%Y A182631 Level j=3 column k=0 of tetrahedron = column 4 of triangle gives A008585.
%Y A182631 Level j=3 column k=1 of tetrahedron = column 5 of triangle gives A016777.
%Y A182631 Level j=3 column k=2 of tetrahedron = column 6 of triangle gives A016789.
%Y A182631 And so on.
%K A182631 nonn,tabf
%O A182631 0,5
%A A182631 _Omar E. Pol_, Dec 06 2010