A279229 - OEIS

A279229

Odd orders n for which a complete dihedral Hamiltonian cycle system of the cocktail graph exists.

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..51.

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

Adjacent sequences: A279226 A279227 A279228 * A279230 A279231 A279232

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Jan 04 2017

STATUS

approved