# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a182631 Showing 1-1 of 1 %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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE