|
| |
|
|
A000341
|
|
Number of ways to pair up {1..2n} so sum of each pair is prime.
|
|
10
|
|
|
|
1, 2, 3, 6, 26, 96, 210, 1106, 3759, 12577, 74072, 423884, 2333828, 16736611, 99838851, 630091746, 4525325020, 38848875650, 342245714017, 3335164762941, 31315463942337, 241353231085002, 2350106537365732, 17903852593938447, 158065352670318614, 1815064841856534244, 20577063085601738871, 276081763499377227299
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
Table of n, a(n) for n=1..28.
L. E. Greenfield and S. J. Greenfield, Some Problems of Combinatorial Number Theory Related to Bertrand's Postulate, J. Integer Sequences, 1998, #98.1.2.
|
|
|
FORMULA
|
a(n) = permanent(m), where the n X n matrix m is defined by m(i,j) = 1 or 0, depending on whether 2i+2j-1 is prime or composite, respectively. - T. D. Noe, Feb 10 2007
|
|
|
EXAMPLE
|
For n=4, there are 6 ways to pair up {1, 2, 3, 4, 5, 6, 7, 8} so that each pair sums to a prime:
1+2, 3+4, 5+8, 6+7
1+2, 3+8, 4+7, 5+6
1+4, 2+3, 5+8, 6+7
1+4, 2+5, 3+8, 6+7
1+6, 2+3, 4+7, 5+8
1+6, 2+5, 3+8, 4+7
Therefore a(4) = 6. - Michael B. Porter, Jul 19 2016
|
|
|
MAPLE
|
f:= proc(n) local M;
M:= Matrix(n, n, (i, j) -> `if`(isprime(2*i+2*j-1), 1, 0));
LinearAlgebra:-Permanent(M)
end proc:
map(f, [$1..20]); # Robert Israel, Jul 19 2016
|
|
|
MATHEMATICA
|
a[n_] := Permanent[ Array[ Boole[ PrimeQ[2*#1 + 2*#2 - 1]] & , {n, n}]]; Table[an = a[n]; Print[an]; an, {n, 1, 20}] (* Jean-François Alcover, Oct 21 2011, after T. D. Noe, updated Feb 07 2016 *)
|
|
|
PROG
|
(PARI) permRWNb(a)=n=matsize(a)[1]; if(n==1, return(a[1, 1])); sg=1; nc=0; in=vectorv(n); x=in; x=a[, n]-sum(j=1, n, a[, j])/2; p=prod(i=1, n, x[i]); for(k=1, 2^(n-1)-1, sg=-sg; j=valuation(k, 2)+1; z=1-2*in[j]; in[j]+=z; nc+=z; x+=z*a[, j]; p+=prod(i=1, n, x[i], sg)); return(2*(2*(n%2)-1)*p)
for(n=1, 24, a=matrix(n, n, i, j, isprime(2*(i+j)-1)); print1(permRWNb(a)", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 13 2007
|
|
|
CROSSREFS
|
Cf. A005326, A009692.
Sequence in context: A333420 A296259 A344935 * A144857 A090445 A228346
Adjacent sequences: A000338 A000339 A000340 * A000342 A000343 A000344
|
|
|
KEYWORD
|
nonn,nice
|
|
|
AUTHOR
|
S. J. Greenfield (greenfie(AT)math.rutgers.edu)
|
|
|
EXTENSIONS
|
More terms from David W. Wilson
More terms from T. D. Noe, Feb 10 2007
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 13 2007
More terms from Sean A. Irvine, Nov 14 2010
|
|
|
STATUS
|
approved
|
| |
|
|
