A348824 Numbers in array A327259 that do not have a unique decomposition into numbers of A327261.
32, 48, 72, 96, 112, 126, 128, 144, 160, 168, 176, 192, 198, 221, 224, 240, 252, 256, 264, 288, 294, 304, 336, 342, 347, 352, 360, 368, 384, 392, 396, 414, 416, 432, 448, 456, 462, 480, 496, 504, 512, 528, 544, 545, 552, 558, 560, 576, 588, 599
Offset: 1
Keywords
Examples
48 is in the sequence because 48 = A327259(2,12) = A327259(4,6) and 2, 4, 6 and 12 are in A327261. 72 is in the sequence because 72 = A327259(2,2,5) = A327259(6,6) and 2, 5 and 6 are in A327261. A327259(2,2,5) is well-defined because A327259(n,k) is associative. 221 is in the sequence because 221 = A327259(5,25) = A327259(11,11) and 5, 11 and 25 are in A327261. 462 is in the sequence because 462 = A327259(6,39) = A327259(11,22) = A327259(14,17) and 6, 11, 14, 17, 22 and 39 are in A327261. The first six terms and their decompositions: 1 32 = A327259(2,2,2) = A327259(4,4) 2 48 = A327259(2,12) = A327259(4,6) 3 72 = A327259(2,2,5) = A327259(6,6) 4 96 = A327259(2,2,6) = A327259(4,12) 5 112 = A327259(2,28) = A327259(4,14) 6 126 = A327259(5,14) = A327259(6,11) More in a-file.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..1256 (all terms m <= 10000)
- David Lovler, Decomposition of a(n) into A327261(k)
Programs
-
Mathematica
T[n_,k_]:=2n*k-If[Mod[n,2]==1,If[Mod[k,2]==1,n+k-1,k],If[Mod[k,2]==1,n,0]];F[d_]:=If[(q=Union[Sort/@(Position[Table[T[n,k],{n,2,Ceiling[d/3]},{k,2,Ceiling[d/3]}],d]+1)])=={},{{d}},q];FC[x_]:=FixedPoint[Union[Sort/@Flatten[Flatten/@Tuples[#]&/@((F/@#&/@#)&[#]),1]]&,F[x]];list={};Do[If[Length@FC@i>1,AppendTo[list,i]],{i,300}];list (* Giorgos Kalogeropoulos, Nov 05 2021 *)
Extensions
Name amended by David Lovler, Jan 26 2022
Comments