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 A204016 Symmetric matrix based on f(i,j)=max{j mod i, i mod j), by antidiagonals. 74
 0, 1, 1, 1, 0, 1, 1, 2, 2, 1, 1, 2, 0, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 3, 0, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 0, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 0, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 0, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 7 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS A204016 represents the matrix M given by f(i,j)=max{(j mod i), (i mod j)} for i>=1 and j>=1.  See A204017 for characteristic polynomials of principal submatrices of M, with interlacing zeros. Guide to symmetric matrices M based on functions f(i,j) and characteristic polynomial sequences (c.p.s.) with interlaced zeros: f(i,j).......................M.........c.p.s. C(i+j,j).....................A007318...A045912 min(i,j).....................A003983...A202672 max(i,j).....................A051125...A203989 (i+j)*min(i,j)...............A203990...A203991 |i-j|........................A049581...A203993 max(i-j+1,j-i+1).............A143182...A203992 min(i-j+1,j-i+1).............A203994...A203995 min(i(j+1),j(i+1))...........A203996...A203997 max(i(j+1)-1,j(i+1)-1).......A203998...A203999 min(i(j+1)-1,j(i+1)-1).......A204000...A204001 min(2i+j,i+2j)...............A204002...A204003 max(2i+j-2,i+2j-2)...........A204004...A204005 min(2i+j-2,i+2j-2)...........A204006...A204007 max(3i+j-3,i+3j-3)...........A204008...A204011 min(3i+j-3,i+3j-3)...........A204012...A204013 min(3i-2,3j-2)...............A204028...A204029 1+min(j mod i, i mod j)......A204014...A204015 max(j mod i, i mod j)........A204016...A204017 1+max(j mod i, i mod j)......A204018...A204019 min(i^2,j^2).................A106314...A204020 min(2i-1, 2j-1)..............A157454...A204021 max(2i-1, 2j-1)..............A204022...A204023 min(i(i+1)/2,j(j+1)/2).......A106255...A204024 GCD(i,j).....................A003989...A204025 GCD(i+1,j+1).................A204030...A204111 min(F(i+1),F(j+1),F=A000045..A204026...A204027 GCD(F(i+1),F(j+1),F=A000045..A204112...A204113 GCD(L(i),L(j),L=A000032......A204114...A204115 GCD(2^i-1,2^j-2).............A204116...A204117 GCD(prime(i),prime(j)).......A204118...A204119 GCD(prime(i+1),prime(j+1))...A204120...A204121 GCD(2^(i-1),2^(j-1)).........A144464...A204122 max(floor(i/j),floor(j/i))...A204123...A204124 min(ceil(i/j),ceil(j/i)).....A204143...A204144 Delannoy matrix..............A008288...A204135 max(2i-j,2j-i)...............A204154...A204155 -1+max(3i-j,3j-i)............A204156...A204157 max(3i-2j,3j-2i).............A204158...A204159 floor[(i+1)/2]...............A204164...A204165 ceiling[(i+1)/2].............A204166...A204167 i+j..........................A003057...A204168 i+j-1........................A002024...A204169 i*j..........................A003991...A204170 ..abbreviation below:  AOE means "all 1's except" AOE f(i,i)=i.................A204125...A204126 AOE f(i,i)=A000045(i+1)......A204127...A204128 AOE f(i,i)=A000032(i)........A204129...A204130 AOE f(i,i)=2i-1..............A204131...A204132 AOE f(i,i)=2^(i-1)...........A204133...A204134 AOE f(i,i)=3i-2..............A204160...A204161 AOE f(i,i)=floor[(i+1)/2]....A204162...A204163 ... Other pairs (M, c.p.s.): (A204171, A204172) to (A204183, A204184) See A202695 for a guide to choices of symmetric matrix M for which the zeros of the characteristic polynomials are all positive. LINKS EXAMPLE Northwest corner: 0 1 1 1 1 1 1 1 0 1 2 2 2 2 2 2 1 2 0 3 3 3 3 3 1 2 3 0 4 4 4 4 1 2 3 4 0 5 5 5 1 2 3 4 5 0 6 6 1 2 3 4 5 6 0 7 MATHEMATICA f[i_, j_] := Max[Mod[i, j], Mod[j, i]]; m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}] TableForm[m[8]] (* 8x8 principal submatrix *) Flatten[Table[f[i, n + 1 - i], {n, 1, 12}, {i, 1, n}]]  (* A204016 *) p[n_] := CharacteristicPolynomial[m[n], x]; c[n_] := CoefficientList[p[n], x] TableForm[Flatten[Table[p[n], {n, 1, 10}]]] Table[c[n], {n, 1, 12}] Flatten[%]               (* A204017 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A204017, A202453. Sequence in context: A214810 A257248 A090737 * A157865 A274274 A072550 Adjacent sequences:  A204013 A204014 A204015 * A204017 A204018 A204019 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jan 10 2012 STATUS approved

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Last modified November 17 14:18 EST 2018. Contains 317276 sequences. (Running on oeis4.)