A067276 -id:A067276 - cp's OEIS frontend

A119498 Consider the sign of A067276: determinant of n X n matrix containing the first n^2 primes in increasing order; then a(n) = 0 if negative and 1 if positive.

1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1

Offset: 1

Robert G. Wilson v, May 26 2006

nonn

The determinant of A can never be 0 since there is an even prime in the mix.
Conjecture: This sequence never cycles.
Positions where the race between the zeros and the ones is tied: 2,4,16,34,36,38,40,42,46,66,78,80,82,84, ...,.

Cf. A000040, A067276.

f[n_] := Sign@ Det@ Partition[ Array[Prime, n^2], n]; Array[f, 105] /. -1 -> 0

A023999 Absolute value of determinant of n X n matrix whose entries are the integers from 1 to n^2 spiraling inward, starting in a corner.

Original entry on oeis.org

1, 5, 48, 660, 11760, 257040, 6652800, 198918720, 6745939200, 255826771200, 10727081164800, 492775291008000, 24610605962342400, 1327677426915840000, 76940526008586240000, 4766815315895592960000, 314406967644177408000000, 21995911456386651463680000

Offset: 1

Charles Diminnie (charles.diminnie(AT)rampo.angelo.edu)

nonn

Starting in the NW or SE corner, the signs are cyclic (+,-,-,+), starting in the NE or SW corner, the signs are always positive.

			n=4: det of
.1..2..3.4
12.13.14.5
11.16.15.6
10..9..8.7

Alois P. Heinz, Table of n, a(n) for n = 1..200
Gaurav Bhatnagar, Christian Krattenthaler, Spiral determinants, arXiv:1704.02859 [math.CO], 2017.
Charles Vanden Eynden, Problem 1517, Mathematics Magazine, Vol. 70, No. 1, Feb., 1997 p. 65.

Cf. A079340, A078475, A067276, A052182.

Main diagonal of A226167, A126224 (signed version). - Alois P. Heinz, Jan 21 2014

a:= proc(n) option remember; `if`(n<2, (3*n+1)/4,
      4*(3*n-1)*(2*n-5)*(2*n-3) *a(n-2) /(3*n-7))
    end:
seq(a(n), n=1..20);  # Alois P. Heinz, Jan 21 2014

M[0, 0] = 1;
M[i_, j_] := If[i <= j,
  If[i + j >= 0, If[i != j, M[i + 1, j] + 1, M[i, j - 1] + 1],
   M[i, j + 1] + 1],
  If[i + j > 1, M[i, j - 1] + 1, M[i - 1, j] + 1]
  ]
M[n_] := n^2 + 1 - If[EvenQ[n],
  Table[M[i, j], {j, n/2, -n/2 + 1, -1}, {i, -n/2 + 1, n/2}],
  Table[M[i, j], {j, (n - 1)/2, -(n - 1)/2, -1}, {i, -(n - 1)/2, (n - 1)/2}]]
a[n_]:=Det[M[n]] (* Christian Krattenthaler, Apr 19 2017 *)

A023999(n):=if n=1 then 1 else 2*((-1)^((n+4)*(n-1))/2 *(3*n-1) * (2*n-3)!/(n-2)!)$
makelist(A023999(n),n,1,30); /* Martin Ettl, Nov 05 2012 */

a(n) = (3n-1) * (2n-3)!/(n-2)! for n >= 2. [corrected by Robert Israel, Apr 20 2017]

E.g.f.: ((-2*x-1)*sqrt(1-4*x)+1-4*x)/(16*x-4). - Robert Israel, Apr 20 2017

Edited and extended by Robert G. Wilson v, May 07 2003

A114533 Permanent of the n X n matrix with numbers prime(1),prime(2),...,prime(n^2) in order across rows.

Original entry on oeis.org

1, 2, 29, 3746, 1919534, 2514903732, 6571874957648, 30662862975835376, 228731722381012564816, 2641049525155781555257440, 43818773386947889568479502592, 1014966115357067575070490776083200, 31412851866841234377483875199638978304

Offset: 0

Simone Severini, Feb 15 2006

nonn

Previous name was : "a(n) = permanent of the n X n matrix M defined as follows: if we concatenate the rows of M to form a vector v of length n^2, v_i is the i-th prime number".

Vaclav Kotesovec, Table of n, a(n) for n = 0..36 (terms 0..20 from Alois P. Heinz)

Cf. A067276, A232773.

with(LinearAlgebra):
a:= n->`if`(n=0, 1, Permanent(Matrix(n, (i, j)->ithprime((i-1)*n+j)))):
seq(a(n), n=0..12);  # Alois P. Heinz, Dec 23 2013

a[n_] := Permanent[Table[Prime[(i-1)*n+j], {i, 1, n}, {j, 1, n}]]; a[0]=1; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 12}] (* Jean-François Alcover, Jan 07 2016, adapted from Maple *)
Join[{1},Table[Permanent[Partition[Prime[Range[n^2]],n]],{n,15}]] (* Harvey P. Dale, Aug 03 2019 *)

permRWN(a)=n=matsize(a)[1]; if(n==1,return(a[1,1])); n1=n-1; sg=1; m=1; nc=0; in=vector(n); x=in; for(i=1,n,x[i]=a[i,n]-sum(j=1,n,a[i,j])/2); p=prod(i=1,n,x[i]); while(m,sg=-sg; j=1; if((nc%2)!=0,j++; while(in[j-1]==0,j++)); in[j]=1-in[j]; z=2*in[j]-1; nc+=z; m=nc!=in[n1]; for(i=1,n,x[i]+=z*a[i,j]); p+=sg*prod(i=1,n,x[i])); return(2*(2*(n%2)-1)*p)
for(n=1,19,a=matrix(n,n,i,j,prime((i-1)*n+j)); print1(permRWN(a)", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 11 2007

permRWNb(a)=n=matsize(a)[1];if(n==1,return(a[1,1]));sg=1;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;x+=z*a[,j];p+=prod(i=1,n,x[i],sg));return(2*(2*(n%2)-1)*p)
for(n=1,23,a=matrix(n,n,i,j,prime((i-1)*n+j));print1(permRWNb(a)",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 15 2007

{a(n) = matpermanent(matrix(n, n, i, j, prime((i-1)*n+j)))}
for(n=0, 25, print1(a(n), ", ")) \\ Vaclav Kotesovec, Aug 13 2021

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 11 2007
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 15 2007
New name from Michel Marcus, Nov 30 2013
a(0) inserted and a(12) by Alois P. Heinz, Dec 23 2013

A118770 Determinant of n X n matrix containing the first n^2 semiprimes in increasing order.

Original entry on oeis.org

4, -14, -196, 480, 696, -57901, -525364, -409579, 18528507, -237549252, -2119519900, 6713972874, 18262155072, -19072020914992, 162234208372185, 1471912942112734, 6828673030820538, -35126752028893500, 729026655790306778, -15365360727898374618

Offset: 1

Jonathan Vos Post, May 22 2006

Semiprime analog of A067276 Determinant of n X n matrix containing the first n^2 primes in increasing order. The first column contains the first n semiprimes in increasing order, the second column contains the next n semiprimes in increasing order, etc. Equivalently, first row contains first n semiprimes in increasing order, second row contains next n semiprimes in increasing order, etc. See also: A118713 a(n) = determinant of n X n circulant matrix whose first row is A001358(1), A001358(2), ..., A001358(n) where A001358(n) = n-th semiprime.

			a(2) = -14 because of the determinant -14 =
|4,6 |
|9,10|.
a(6) = -57901 = the determinant
|4, 6, 9, 10, 14, 15,|
|21, 22, 25, 26, 33, 34,|
|35, 38, 39, 46, 49, 51,|
|55, 57, 58, 62, 65, 69,|
|74, 77, 82, 85, 86, 87,|
|91, 93, 94, 95, 106, 111|.

Harvey P. Dale, Table of n, a(n) for n = 1..570

Cf. A001358, A067276, A118713, A118772, A118779.

SemiPrimePi[ n_ ] := Sum[ PrimePi[ n/Prime @ i ] - i + 1, {i, PrimePi @ Sqrt @ n} ]; SemiPrime[ n_ ] := Block[ {e = Floor[ Log[ 2, n ] + 1 ], a, b}, a = 2^e; Do[ b = 2^p; While[ SemiPrimePi[ a ] < n, a = a + b ]; a = a - b/2, {p, e, 0, -1} ]; a + b/2 ]; Table[ Det[ Partition[ Array[ SemiPrime, n^2 ], n ] ], {n, 20} ] (* Robert G. Wilson v, May 26 2006 *)
Module[{nn=5000,spr},spr=Select[Range[nn],PrimeOmega[#]==2&];Table[Det[ Partition[ Take[spr,n^2],n]],{n,Sqrt[Length[spr]]}]] (* Harvey P. Dale, Nov 21 2018 *)

More terms from Robert G. Wilson v, May 26 2006

Typos in Mma program corrected by Giovanni Resta, Jun 12 2016

A118799 Determinants of 4 X 4 matrices of 16 consecutive primes.

Original entry on oeis.org

880, -448, -1472, -240, 2480, -1352, -4128, -96, 2736, -2520, 120, 1080, 4288, 4880, 4600, 13368, 7056, 14560, 2960, 13320, 0, 24864, -11096, -24264, 0, -9168, -2128, -15792, 0, 18120, -5248, 6384, -21840, -38776, -20480, 20176, -72896, -69200, 40080, -37632

Offset: 1

Jonathan Vos Post, May 23 2006

4 X 4 analog of A117330.

All terms are even. - Harvey P. Dale, May 05 2016

			a(1) = 880 =
  | 2  3  5  7|
  |11 13 17 19|
  |23 29 31 37|
  |41 43 47 53|.
a(10) = -2520 =
  |29 31 37 41|
  |43 47 53 59|
  |61 67 71 73|
  |79 83 89 97|.
a(21) = 0 =
  | 73  79  83  89|
  | 97 101 103 107|
  |109 113 127 131|
  |137 139 149 151|.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000040, A067276, A117301, A117330 , A118713.

A118799 := proc(n)
    local A,i,r,c ;
    A := Matrix(4,4) ;
    i := n ;
    for r from 1 to 4 do
    for c from 1 to 4 do
        A[r,c] := ithprime(i) ;
        i := i+1 ;
    end do:
    end do:
    LinearAlgebra[Determinant](A) ;
end proc: # R. J. Mathar, May 05 2013

Module[{nn=60,prs},prs=Prime[Range[nn]];Table[Det[Partition[ Take[ prs, {n,n+15}],4]],{n,nn-15}]] (* Harvey P. Dale, Apr 29 2016 *)

a(n) = matdet(matrix(4,4,i,j,prime((n+j-1)+4*(i-1)))); \\ Michel Marcus, Jan 25 2021

A079340 Absolute value of determinant of n X n matrix whose entries are the integers from 1 to n^2 spiraling outward, ending in a corner.

Original entry on oeis.org

1, 5, 72, 1380, 31920, 861840, 26611200, 925404480, 35805369600, 1526139014400, 71066912716800, 3590219977344000, 195589552648089600, 11430978821982720000, 713448513897799680000, 47363888351558338560000

Offset: 1

Kit Vongmahadlek (kit119(AT)yahoo.com), Jan 03 2003

If n == 0 or 1 (mod 4), the sign of the determinant will be independent of the orientation of the spiral. For n == 2 or 3 (mod 4), the sign will be reversed when the orientation is rotated by 1/4 or flipped on the horizontal or vertical axis. - Franklin T. Adams-Watters, Dec 31 2013

This distribution of the integers is sometimes known as Ulam's spiral, although that is sometimes reserved for when the primes are marked out in some way. - Franklin T. Adams-Watters, Dec 31 2013

			n=2, det=-5: {1 2 / 4 3 }.
n=3, det=72: {7 8 9 / 6 1 2 / 5 4 3 }.
n=4, det=-1380: { 7 8 9 10 / 6 1 2 11 /5 4 3 12 / 16 15 14 13 }.
n=5, det=31920: { 21 22 23 24 25 / 20 7 8 9 10 / 19 6 1 2 11 /18 5 4 3 12 / 17 16 15 14 13 }

Gaurav Bhatnagar, Christian Krattenthaler, Spiral determinants, arXiv:1704.02859 [math.CO], 2017.

Cf. A078475, A023999, A067276, A052182.

M[0, 0] = 1;
M[i_, j_] := If[i <= j,
  If[i + j >= 0, If[i != j, M[i + 1, j] + 1, M[i, j - 1] + 1],
   M[i, j + 1] + 1],
  If[i + j > 1, M[i, j - 1] + 1, M[i - 1, j] + 1]
  ]
M[n_] := If[EvenQ[n],
  Table[M[i, j], {j, n/2, -n/2 + 1, -1}, {i, -n/2 + 1, n/2}],
  Table[M[i, j], {j, (n - 1)/2, -(n - 1)/2, -1}, {i, -(n - 1)/2, (n - 1)/2}]]
a[n_]:=Det[M[n]] (* Christian Krattenthaler, Apr 19 2017 *)

A079340(n):=if n=1 then 1 else (2*n^2-3*n+3)*(2*n-2)!/(2*(n-1)!)$
makelist(A079340(n),n,1,30); /* Martin Ettl, Nov 05 2012 */

a(n) = (2*n^2-3*n+3) (2n-2)!/(2 (n-1)!) = A096376(n-1)*A000407(n-2), n>1. - Conjectured by Dean Hickerson, Jan 30 2003. Proved in the article by Bhatnagar and Krattenthaler.

D-finite with recurrence (2*n^2-7*n+8)*a(n) -2*(2*n-3)*(2*n^2-3*n+3)*a(n-1)=0. - R. J. Mathar, May 03 2019

Extended by Robert G. Wilson v, Jan 25 2003

A118772 Determinant of n X n matrix containing the first n^2 3-almost primes in increasing order.

Original entry on oeis.org

8, -56, 156, 13328, -920, -83678, 1261988, 54252742, 214409844, -3528354250, 247094703588, -509185323508, 15154985424718, 884710401396570, 49777180907707320, -172913218088289027, 844641410704177098, 3066058962037715903, -33948947842497666568

Offset: 1

Jonathan Vos Post, May 22 2006

3-almost prime analog of A067276 Determinant of n X n matrix containing the first n^2 primes in increasing order. The first column contains the first n 3-almost primes in increasing order, the second column contains the next n 3-almost primes in increasing order, etc. Equivalently, first row contains first n 3-almost primes in increasing order, second row contains next n 3-almost primes in increasing order, etc. See also: A118713 a(n) = semiprime circulant.

			a(2) = -56 because of the determinant -56 =
|8, 12|
18, 20|.
a(6) = -83678 because of the determinant -83678 =
| 8, 12, 18, 20, 27, 28|
| 30, 42, 44, 45, 50, 52|
| 63, 66, 68, 70, 75, 76|
| 78, 92, 98, 99, 102, 105|
| 110, 114, 116, 117, 124, 125|
| 130, 138, 147, 148, 153, 154|.

Cf. A014612, A067276, A118713, A118770, A118779.

ThreeAlmostPrimePi[ n_ ] := Sum[ PrimePi[ n/(Prime @ i*Prime @ j) ] - j + 1, {i, PrimePi[ n^(1/3) ]}, {j, i, PrimePi@ Sqrt[ n/Prime @ i ]} ]; ThreeAlmostPrime[ n_ ] := Block[ {e = Floor[ Log[ 2, n ] + 1 ], a, b}, a = 2^e; Do[ b = 2^p; While[ ThreeAlmostPrimePi[ a ] < n, a = a + b ]; a = a - b/2, {p, e, 0, -1} ]; a + b/2 ]; Table[ Det[ Partition[ Array[ ThreeAlmostPrime, n^2 ], n ] ], {n, 19} ] (* Robert G. Wilson v, May 26 2006 *)
With[{tap=Select[Range[4000],PrimeOmega[#]==3&]},Table[Det[ Partition[ Take[tap,n^2],n]],{n,20}]] (* Harvey P. Dale, Apr 17 2020 *)

More terms from Robert G. Wilson v, May 26 2006

Typos in Mma program corrected by Giovanni Resta, Jun 12 2016

A118779 Determinant of n X n matrix containing the first n^2 4-almost primes in increasing order.

Original entry on oeis.org

16, -224, 0, 182016, 12734992, -80430368, -125120640, 1334967760, 1060202222660, -2759409121760, 54820105989504, -14148083510835712, 49989643415528010, 299304923505836144, 1713123391839442498, 93227182153040103540, -86403659709730762670

Offset: 1

Jonathan Vos Post, May 22 2006

4-almost prime analog of A067276 Determinant of n X n matrix containing the first n^2 primes in increasing order. The first column contains the first n 4-almost primes (A014613) in increasing order, the second column contains the next n 4-almost primes in increasing order, etc. Equivalently, first row contains first n 4-almost primes in increasing order, second row contains next n 4-almost primes in increasing order, etc. See also: A118713 a(n) = semiprime circulant.

			a(2) = -224 because of the determinant -224 =
|16, 24|
|36, 40|.
a(3) = 0 because this matrix is singular: 0 =
|16, 24, 36|
|40, 54, 56|
|60, 81, 84|.
a(6) = -80430368 because of the determinant -80430368 =
| 16, 24, 36, 40, 54, 56|
| 60, 81, 84, 88, 90, 100|
| 104, 126, 132, 135, 136, 140|
| 150, 152, 156, 184, 189, 196|
| 198, 204, 210, 220, 225, 228|
| 232, 234, 248, 250, 260, 276|.
a(8) = 1334967760 =
| 16, 24, 36, 40, 54, 56, 60, 81|
| 84, 88, 90, 100, 104, 126, 132, 135|
|136, 140, 150, 152, 156, 184, 189, 196|
|198, 204, 210, 220, 225, 228, 232, 234|
|248, 250, 260, 276, 294, 296, 297, 306|
|308, 315, 328, 330, 340, 342, 344, 348|
|350, 351, 364, 372, 375, 376, 380, 390|
|414, 424, 441, 444, 459, 460, 462, 472|.

Cf. A014613, A118713, A067276, A118770, A118772.

FourAlmostPrimePi[n_] := Sum[PrimePi[n/(Prime@i*Prime@j*Prime@k)] - k + 1, {i, PrimePi[n^(1/4)]}, {j, i, PrimePi[(n/Prime@i)^(1/3)]}, {k, j, PrimePi@Sqrt[n/(Prime@i*Prime@j)]}]; FourAlmostPrime[n_] := Block[{e = Floor[Log[2, n] + 1], a, b}, a = 2^e; Do[b = 2^p; While[FourAlmostPrimePi[a] < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; Table[Det[Partition[Array[FourAlmostPrime, n^2], n]], {n, 17}] (* Robert G. Wilson v, May 26 2006 *)

More terms from Robert G. Wilson v, May 26 2006

A118780 Semiprime(n)semiprime(n+3) - semiprime(n+1)semiprime(n+2), where semiprime(n) is the n-th semiprime.

Original entry on oeis.org

-14, -6, -5, 0, -7, -87, -4, 76, -8, -212, 64, -4, 128, 68, -265, 31, -12, -177, 104, 109, -28, 103, -101, -40, -24, -348, -176, 253, 81, -285, -97, 928, 364, -841, -257, -361, -127, -3, -125, 603, 359, -675, 367, -8, -860, 139, -3, 995, 280, -1276, -167, 629, 145, 443, -365, -579, 171, -569

Offset: 1

Jonathan Vos Post, May 22 2006

Semiprime analog of A117301.

By construction, every entry is also the difference between two 4-almost primes: a(1) = A014613(4)-A014613(5); a(2) = A014613(9)-A014613(11); a(3) = A014613(16)-A014613(18); a(4) = A014613(27)-A014613(27); etc. - R. J. Mathar, Nov 27 2007

			a(1) = -14 because the determinant of the first block of 4 consecutive semiprimes is:
|4. 6.|
|9. 10|.
a(4) = 0 because the determinant of the 4th block of 4 semiprimes is the first of a presumably infinite number of singular matrices:
|10. 14.|
|15. 21.|.
a(8) = 76, the first positive value in the sequence:
|22. 25.|
|26. 33.|.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001358, A067276, A117301, A118713.

A001358 := proc(n) option remember ; local a; if n = 1 then 4 ; else for a from A001358(n-1)+1 do if numtheory[bigomega](a)= 2 then RETURN(a) ; fi ; od: fi ; end: A118780 := proc(n) A001358(n)*A001358(n+3)-A001358(n+1)*A001358(n+2) ; end: seq(A118780(n),n=1..58) ; # R. J. Mathar, Nov 27 2007

nmax = 58; spmax = nmax; SP = {};
While[nmax+3 > Length[SP], spmax += nmax; SP = Select[Range[spmax], PrimeOmega[#] == 2&]];
a[n_] := SP[[n]] SP[[n+3]] - SP[[n+1]] SP[[n+2]];
Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Aug 01 2023 *)
#[[1]]#[[4]]-#[[2]]#[[3]]&/@Partition[Select[Range[300],PrimeOmega[#]==2&],4,1] (* Harvey P. Dale, Sep 08 2024 *)

a(n) = A001358(n)*A001358(n+3) - A001358(n+1)*A001358(n+2).

Better definition from Jens Kruse Andersen, May 03 2008

A118781 Determinants of 3 X 3 matrices of continuous blocks of 9 consecutive semiprimes.

Original entry on oeis.org

-196, 272, -251, 149, -423, 909, -408, -452, 958, -123, -112, -460, 84, -271, -187, -162, 63, 7, 101, -483, -133, 205, -860, -46, 339, 1178, 848, 366, 1084, 719, -384, 334, -2736, -984, -1912, 214, 34, 40, -1735, -60, 64, -2263, -3468, 5795, 69, 132, 3007, 256, 2130, 3428

Offset: 1

Jonathan Vos Post, May 22 2006

Semiprime analog of A117330 Determinants of 3 X 3 matrices of continuous blocks of 9 consecutive primes. The terminology "continuous" is used to distinguish from "discrete" which would be (in this 3 X 3 semiprime case) block 1: 4, 6, 9, 10, 14, 15, 21, 22, 25; block 2: 26, 33, 34, 35, 38, 39, 46, 49, 51; and so forth.

			a(1) = -196 because the determinant of the first continuous block of 9 semiprimes is:
| 4. 6. 9.|
|10. 14. 15.|
|21. 22. 25.|.
a(9) = 958 because the determinant of the 9th continuous block of 9 semiprimes is:
|25. 26. 33.|
|34. 35. 38.|
|39. 46. 49.|.
a(50) = 3428 because the determinant of the 50th continuous block of 9 semiprimes is:
|146. 155. 158.|
|159. 161. 166.|
|169. 177. 178.|.

Cf. A001358, A067276, A117301, A118713.

A118781 := proc(n)
    local A,i,r,c ;
    A := Matrix(3,3) ;
    i := n ;
    for r from 1 to 3 do
    for c from 1 to 3 do
        A[r,c] := A001358(i) ;
        i := i+1 ;
    end do:
    end do:
    LinearAlgebra[Determinant](A) ;
end proc: # R. J. Mathar, May 05 2013

Det/@(Partition[#,3]&/@(Partition[Select[Range[200],PrimeOmega[ #] == 2&],9,1])) (* Harvey P. Dale, Nov 29 2015 *)

a(n) = s(n)*s(n+4)*s(n+8) - s(n)*s(n+5)*s(n+7) - s(n+1)*s(n+3)*s(n+8) + s(n+1)*s(n+5)*s(n+6) + s(n+2)*s(n+3)*s(n+7) - s(n+2)*s(n+4)*s(n+6) where s(n) = A001358(n) is the n-th semiprime.

cp's OEIS Frontend

A119498 Consider the sign of A067276: determinant of n X n matrix containing the first n^2 primes in increasing order; then a(n) = 0 if negative and 1 if positive.

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A023999 Absolute value of determinant of n X n matrix whose entries are the integers from 1 to n^2 spiraling inward, starting in a corner.

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Maple

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Maxima

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A114533 Permanent of the n X n matrix with numbers prime(1),prime(2),...,prime(n^2) in order across rows.

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PARI

PARI

PARI

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A118770 Determinant of n X n matrix containing the first n^2 semiprimes in increasing order.

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Mathematica

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A118799 Determinants of 4 X 4 matrices of 16 consecutive primes.

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Maple

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PARI

A079340 Absolute value of determinant of n X n matrix whose entries are the integers from 1 to n^2 spiraling outward, ending in a corner.

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Mathematica

Maxima

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A118772 Determinant of n X n matrix containing the first n^2 3-almost primes in increasing order.

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A118780 Semiprime(n)semiprime(n+3) - semiprime(n+1)semiprime(n+2), where semiprime(n) is the n-th semiprime.