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A279229
Odd orders n for which a complete dihedral Hamiltonian cycle system of the cocktail graph exists.
0
21, 33, 45, 57, 65, 69, 77, 85, 93, 105, 117, 123, 129, 133, 141, 145, 153, 161, 165, 177, 185, 189, 201, 209, 213, 217, 219, 221, 225, 237, 245, 249, 253, 261, 265, 267, 273, 285, 287, 291, 297, 301, 305, 309, 321, 325, 329, 333, 341, 345, 357
OFFSET
1,1
LINKS
M. Buratti and F. Merola, Dihedral Hamiltonian cycle systems of the Cocktail Party Graph, J. Combin. Des. 21 (1) (2013) 1-23, Section 3.
MAPLE
isA000961 := proc(n)
local pf;
if n = 1 then
return true;
end if;
pf := ifactors(n)[2] ;
if nops(pf) > 1 then
false;
else
true;
end if ;
end proc:
A023506 := proc(p)
padic[ordp](p-1, 2) ;
end proc:
isA279229 := proc(n)
local ct2, p, l ;
if type(n, 'even') then
false;
elif isA000961(n) then
false;
else
ct2 := 0 ;
for pf in ifactors(n)[2] do
l := A023506(op(1, pf)) ;
ct2 := ct2+l*op(2, pf) ;
end do:
type(ct2, 'even') ;
end if;
end proc:
for n from 2 to 2000 do
if isA279229(n) then
printf("%d, ", n);
end if;
end do:
MATHEMATICA
A023506[p_] := IntegerExponent[p - 1, 2];
isA279229[n_] := Module[{ct2, l}, Which[EvenQ[n], False, PrimePowerQ[n], False, True, ct2 = 0; Do[l = A023506[pf[[1]]]; ct2 = ct2 + l*pf[[2]], {pf, FactorInteger[n]}]; EvenQ[ct2]]];
Select[Range[2, 400], isA279229] (* Jean-François Alcover, Oct 28 2023, after R. J. Mathar's program *)
CROSSREFS
Sequence in context: A273201 A260730 A119973 * A339963 A141249 A026068
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Jan 04 2017
STATUS
approved