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A242528 Number of cyclic arrangements of {0,1,...,n-1} such that both the difference and the sum of any two neighbors are prime. 18
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

Table of n, a(n) for n=1..33.

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}.

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: A275837 A119510 A275725 * A137933 A143116 A115987

Adjacent sequences:  A242525 A242526 A242527 * A242529 A242530 A242531

KEYWORD

nonn,hard,more,changed

AUTHOR

Stanislav Sykora, May 30 2014

EXTENSIONS

a(29)-a(33) from Fausto A. C. Cariboni, May 20 2017

STATUS

approved

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Last modified May 22 16:19 EDT 2017. Contains 286882 sequences.