This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A242528 Number of cyclic arrangements of {0,1,...,n-1} such that both the difference and the sum of any two neighbors are prime. 19
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 18, 13, 62, 8, 133, 225, 209, 32, 2644, 4462, 61341, 113986, 750294, 176301, 7575912, 3575686, 7705362, 36777080, 108638048, 97295807 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 COMMENTS a(n)=NPC(n;S;P) is the count of all neighbor-property cycles for a specific set S of n elements and a specific pair-property P. For more details, see the link and A242519. In this case the set is S={0 through n-1}. For the same pair-property P but the set S={1 through n}, see A227050. LINKS S. Sykora, On Neighbor-Property Cycles, Stan's Library, Volume V, 2014. EXAMPLE For n=12 (the first n for which a(n)>0) there are two such cycles: C_1={0, 5, 2, 9, 4, 1, 6, 11, 8, 3, 10, 7}, C_2={0, 7, 10, 3, 8, 5, 2, 9, 4, 1, 6, 11}. MATHEMATICA A242528[n_] := Count[Map[lpf, Map[j0f, Permutations[Range[n - 1]]]], 0]/2; j0f[x_] := Join[{0}, x, {0}]; lpf[x_] := Length[    Join[Select[asf[x], ! PrimeQ[#] &],     Select[Differences[x], ! PrimeQ[#] &]]]; asf[x_] := Module[{i}, Table[x[[i]] + x[[i + 1]], {i, Length[x] - 1}]]; Table[A242528[n], {n, 1, 8}] (* OR, a less simple, but more efficient implementation. *) A242528[n_, perm_, remain_] := Module[{opt, lr, i, new},    If[remain == {},      If[PrimeQ[First[perm] - Last[perm]] &&        PrimeQ[First[perm] + Last[perm]], ct++];      Return[ct],      opt = remain; lr = Length[remain];      For[i = 1, i <= lr, i++,       new = First[opt]; opt = Rest[opt];       If[! (PrimeQ[Last[perm] - new] && PrimeQ[Last[perm] + new]),        Continue[]];       A242528[n, Join[perm, {new}],        Complement[Range[n - 1], perm, {new}]];       ];      Return[ct];      ];    ]; Table[ct = 0; A242528[n, {0}, Range[n - 1]]/2, {n, 1, 18}] (* Robert Price, Oct 22 2018 *) PROG (C++) See the link. CROSSREFS Cf. A227050, A242519, A242520, A242521, A242522, A242523, A242524, A242525, A242526, A242527, A242529, A242530, A242531, A242532, A242533, A242534. Sequence in context: A119510 A290095 A275725 * A137933 A143116 A304856 Adjacent sequences:  A242525 A242526 A242527 * A242529 A242530 A242531 KEYWORD nonn,hard,more AUTHOR Stanislav Sykora, May 30 2014 EXTENSIONS a(29)-a(33) from Fausto A. C. Cariboni, May 20 2017 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 13 17:16 EST 2018. Contains 317149 sequences. (Running on oeis4.)