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Search: id:A080358
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| A080358 |
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Value of Vandermonde determinant for the first n prime numbers: V[p(1),...,p(n)]. |
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+0
1
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| 1, 1, 6, 240, 414720, 4379443200, 2648687247360000, 11619303595714805760000, 4047756373260469165621248000000, 311107430628520522709128328175943680000000
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OFFSET
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1,3
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COMMENT
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Value of Vandermonde determinant is unchanged if the numbers are shifted by an arbitrary c constant, i.e. v[p(1),...,p(n)]=v[p(1)-c,...,p(n)-c].
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FORMULA
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a(n)=Product[p(i)-p(j)]; i, j, i>j. for n, it is product of C(n, 2) prime differences of not necessarily consecutive primes.
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EXAMPLE
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a(1)=1 corresponds to 1 X 1 V-matrix, while a(2)=1 computed from 2 X 2 matrix.
n = 2: a(2) = p(2)-p(1) = 3-2 = 1; n = 3: a(3) = (5-3)(5-2)(3-2) = 2.3.1 = 6; ... n = 6: a(6) = (13-11).(13-7).(13-5).(13-3).(13-2).(11-7).(11-5).(11-3).(11-2).(7-5).(7-3).(7-2).(5-3).(5-2).(3-2) = 2.6.8.10.11.4.6.8.9.2.4.5.2.3.1 = 10560.1728.40.6.1 = 4379443200
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MATHEMATICA
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b[x_] := Prime[x] d[x_] := b[x+1]-b[x] t[m_] := b[m+1]-Table[b[x], {x, 1, m}] pt[x_] := Apply[Times, t[x]] va[x_] := Apply[Times, Table[pt[w], {w, 1, x}]] Table[va[j], {j, 1, 10}]
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CROSSREFS
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Cf. A000040, A001359.
Sequence in context: A052510 A137892 A064382 this_sequence A156936 A072228 A056238
Adjacent sequences: A080355 A080356 A080357 this_sequence A080359 A080360 A080361
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Feb 19 2003
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