A374067
a(n) is the permanent of the symmetric Toeplitz matrix of order n whose element (i,j) equals the |i-j|-th prime or 1 if i = j.
Original entry on oeis.org
1, 1, 5, 42, 753, 22969, 1226225, 98413280, 11551199289, 1828335971613, 379823112871605, 102232301626742202, 34359550765856135217, 14289766516805617273497, 7224166042347461997365713, 4334493536305030883929928032, 3046742350470292308074313518937, 2492781304663024301187012794633153
Offset: 0
a(4) = 753:
[1, 2, 3, 5]
[2, 1, 2, 3]
[3, 2, 1, 2]
[5, 3, 2, 1]
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a[n_]:=Permanent[Table[ If[i == j, 1, Prime[Abs[i - j]]], {i, 1, n}, {j, 1, n}]]; Join[{1},Array[a, 17]]
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a(n) = matpermanent(matrix(n, n, i, j, if (i==j, 1, prime(abs(i-j))))); \\ Michel Marcus, Jun 27 2024
A374068
a(n) is the permanent of the symmetric Toeplitz matrix of order n whose element (i,j) equals the |i-j|-th prime or 0 if i = j.
Original entry on oeis.org
1, 0, 4, 24, 529, 16100, 919037, 75568846, 9196890092, 1491628025318, 317579623173729, 86997150829931700, 29703399282858184713, 12512837775355494800500, 6397110844644502402189404, 3875565057688532269985283868, 2747710211567246171588232074225, 2265312860218073375019946448731300
Offset: 0
a(4) = 529:
[0, 2, 3, 5]
[2, 0, 2, 3]
[3, 2, 0, 2]
[5, 3, 2, 0]
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a[n_]:=Permanent[Table[If[i == j, 0, Prime[Abs[i - j]]], {i, 1, n}, {j, 1, n}]]; Join[{1},Array[a, 17]]
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a(n) = matpermanent(matrix(n, n, i, j, if (i==j, 0, prime(abs(i-j))))); \\ Michel Marcus, Jun 28 2024
A374070
a(n) is the permanent of the symmetric Toeplitz matrix of order n whose element (i,j) equals the |i-j|-th composite or 0 if i = j.
Original entry on oeis.org
1, 0, 16, 192, 7056, 296928, 17353552, 1288517448, 123247560033, 14559205069230, 2068503986414344, 350413573991639400, 70216794936245622096, 16348540980271313405736, 4358673413318637872138056, 1324443244518891911978887758, 453726273130387432163560157389, 173630294056619179637594095141048
Offset: 0
a(4) = 7056:
[0, 4, 6, 8]
[4, 0, 4, 6]
[6, 4, 0, 4]
[8, 6, 4, 0]
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Composite[n_Integer]:=FixedPoint[n + PrimePi[#] + 1 &, n + PrimePi[n] + 1]; a[n_]:=Permanent[Table[If[i == j, 0, Composite[Abs[i - j]]], {i, 1, n}, {j, 1, n}]]; Join[{1},Array[a,17]]
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a(n) = my(composite(n)=my(k=-1); while(-n+n+=-k+k=primepi(n), ); n); matpermanent(matrix(n, n, i, j, if(i==j, 0, composite(abs(i-j))))); \\ Ruud H.G. van Tol, Jul 14 2024
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from sympy import Matrix, composite
def A374070(n): return Matrix(n,n,[composite(abs(j-k)) if j!=k else 0 for j in range(n) for k in range(n)]).per() if n else 1 # Chai Wah Wu, Jul 01 2024
A374069
a(n) is the permanent of the symmetric Toeplitz matrix of order n whose element (i,j) equals the |i-j|-th composite or 1 if i = j.
Original entry on oeis.org
1, 1, 17, 261, 8393, 356618, 20355656, 1498310848, 141920467648, 16632516446720, 2345863766165536, 394823892589979472, 78653652638945445776, 18216229760067802231488, 4833321599094565894295552, 1462259517864407783009737728, 498935238969900279377677930496, 190227655207141695023381769820864
Offset: 0
a(4) = 8393:
[1, 4, 6, 8]
[4, 1, 4, 6]
[6, 4, 1, 4]
[8, 6, 4, 1]
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Composite[n_Integer]:=FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; a[n_] := Permanent[Table[If[i == j, 1, Composite[Abs[i - j]]], {i, 1, n}, {j, 1, n}]]; Join[{1},Array[a,17]]
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c(n) = for(k=0, primepi(n), isprime(n++)&&k--); n; \\ A002808
a(n) = matpermanent(matrix(n, n, i, j, if (i==j, 1, c(abs(i-j))))); \\ Michel Marcus, Jun 27 2024
Showing 1-4 of 4 results.
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