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Search: id:A000341
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| A000341 |
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Number of ways to pair up {1..2n} so sum of each pair is prime. |
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7
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| 1, 2, 3, 6, 26, 96, 210, 1106, 3759, 12577, 74072, 423884, 2333828, 16736611, 99838851, 630091746, 4525325020, 38848875650, 342245714017, 3335164762941, 31315463942337, 241353231085002, 2350106537365732, 17903852593938447
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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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.
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FORMULA
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a(n)=permanent(m), where the n-by-n matrix m is defined m(i,j) = 1 or 0, depending on whether 2i+2j-1 is prime or composite, respectively. - T. D. Noe (noe(AT)sspectra.com), Feb 10 2007
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PROGRAM
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(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
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CROSSREFS
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Cf. A005326.
Sequence in context: A099000 A032540 A063728 this_sequence A144857 A090445 A018318
Adjacent sequences: A000338 A000339 A000340 this_sequence A000342 A000343 A000344
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KEYWORD
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nonn,nice
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AUTHOR
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S. J. Greenfield, greenfie(AT)math.rutgers.edu
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net).
More terms from T. D. Noe (noe(AT)sspectra.com), Feb 10 2007
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 13 2007
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