The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A213806 Number of minimal coprime labelings for the complete bipartite graph K_{n,n}. 4
 1, 1, 7, 3, 1, 3, 4, 5, 1, 9, 1, 1, 39, 2, 46, 16, 42, 68, 1, 175, 1, 5, 50, 1, 627, 1256, 1177, 10, 1860, 7144, 15, 170, 27156, 178, 64, 2, 6335, 6334, 15592, 4522, 3230, 113926, 99010, 72256, 114606, 199042, 1, 198518, 151036, 236203, 8557, 26542, 21388 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A minimal coprime labeling for K_{n,n} uses two disjoint n-subsets of {1,...,m} with minimal m = A213273(n) >= 2*n as labels for the two disjoint vertex sets such that labels of adjacent vertices are relatively prime.  One of the label sets contains m. LINKS Kevin Cuadrado, Table of n, a(n) for n = 1..105 Adam H. Berliner, N. Dean, J. Hook, A. Marr, A. Mbirika, ​C. McBee, Coprime and prime labelings of graphs, arXiv preprint arXiv:1604.07698 [math.CO], 2016. Eric Weisstein's World of Mathematics, Complete Bipartite Graph FORMULA a(A284875(n)) = 1. - Jonathan Sondow, May 21 2017 EXAMPLE a(1) = 1: the two label sets are {{1}, {2}} with m=2. a(2) = 1: {{1,3}, {2,4}} with m=4. a(3) = 7: {{2,4,5}, {1,3,7}}, {{1,3,5}, {2,4,7}}, {{2,3,4}, {1,5,7}}, {{2,3,6}, {1,5,7}}, {{2,4,6}, {1,5,7}}, {{3,4,6}, {1,5,7}}, {{1,2,4}, {3,5,7}}. a(4) = 3: {{2,4,7,8}, {1,3,5,9}}, {{2,4,5,8}, {1,3,7,9}}, {{1,2,4,8}, {3,5,7,9}}. a(5) = 1: {{2,4,5,8,10}, {1,3,7,9,11}}. a(21) = 1: {{2,4,5,8,10,11,16,20,22,23,25,29,31,32,40,44,46,50,55,58,62}, {1,3,7,9,13,17,19,21,27,37,39,41,43,47,49,51,53,57,59,61,63}}. MAPLE b:= proc(n, k, t, s) option remember;       `if`(nops(s)>=t and k>=t, binomial(nops(s), t),       `if`(n<1, 0, b(n-1, k, t, s)+ b(n-1, k+1, t,       select(x-> x<>n and igcd(n, x)=1, s))))     end: g:= proc(n) option remember; local m, r;       for m from `if`(n=1, 2, g(n-1)[1]) do         r:= b(m-1, 1, n, select(x-> igcd(m, x)=1, {\$1..m-1}));         if r>0 then break fi       od; [m, r]     end: a:= n-> g(n)[2]: seq(a(n), n=1..11); MATHEMATICA b[n_, k_, t_, s_] := b[n, k, t, s] = If[Length[s] >= t && k >= t, Binomial[Length[s], t], If[n < 1, 0, b[n - 1, k, t, s] + b[n - 1, k + 1, t, Select[s, # != n && GCD[n, #] == 1 &]]]]; g[n_] := g[n] = Module[{m, r}, For[ m = If[n == 1, 2, g[n - 1][[1]] ], True, m++, r = b[m - 1, 1, n, Select[Range[1, m - 1], GCD[m, #] == 1 &]]; If [r > 0,  Break[]]]; {m, r}]; a[n_] := a[n] = g[n][[2]]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 18}] (* Jean-François Alcover, Nov 08 2017, after Alois P. Heinz *) CROSSREFS Cf. A213273, A284875, A291465. Sequence in context: A078075 A067616 A199377 * A019856 A124603 A199722 Adjacent sequences:  A213803 A213804 A213805 * A213807 A213808 A213809 KEYWORD nonn AUTHOR Alois P. Heinz, Jun 20 2012 EXTENSIONS Terms a(24) and beyond from Kevin Cuadrado, Dec 01 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 29 11:19 EDT 2021. Contains 346344 sequences. (Running on oeis4.)