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 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 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

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Last modified March 31 14:07 EDT 2023. Contains 361653 sequences. (Running on oeis4.)