|
Search: id:A080358
|
|
|
| A080358 |
|
Value of Vandermonde determinant for the first n prime numbers: V[p(1),...,p(n)]. |
|
+0
1
|
|
| 1, 1, 6, 240, 414720, 4379443200, 2648687247360000, 11619303595714805760000, 4047756373260469165621248000000, 311107430628520522709128328175943680000000
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
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].
|
|
FORMULA
|
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.
|
|
EXAMPLE
|
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
|
|
MATHEMATICA
|
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}]
|
|
CROSSREFS
|
Cf. A000040, A001359.
Sequence in context: A052510 A137892 A064382 this_sequence A072228 A056238 A041853
Adjacent sequences: A080355 A080356 A080357 this_sequence A080359 A080360 A080361
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Labos E. (labos(AT)ana.sote.hu), Feb 19 2003
|
|
|
Search completed in 0.002 seconds
|
