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A127344

Product of 12 consecutive primes.

7420738134810, 152125131763605, 2180460221945005, 20496326086283047, 155186468939000213, 832363787945546597, 3905707004975257109, 15393080549020130959, 57521511525285752531, 182568275710689562381, 497341164867050876831, 1331590860773071702483

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OFFSET

1,1

COMMENTS

a(n) = coefficient of x^0 of the polynomial Prod_{j=0,11}(x-prime(n+j)) of degree 12; the roots of this polynomial are prime(n), ..., prime(n+11).

LINKS

Table of n, a(n) for n=1..12.

MAPLE

A127344 := proc(n) mul(ithprime(n+k), k=0..11) ; end proc: # R. J. Mathar, Apr 05 2011

MATHEMATICA

a = {}; Do[AppendTo[a, Product[Prime[x + n], {n, 0, 11}]], {x, 1, 50}]; a

Times@@@Partition[Prime[Range[50]], 12, 1] (* Harvey P. Dale, Oct 21 2011 *)

PROG

(PARI) {m=10; k=12; for(n=0, m-1, print1(a=prod(j=1, k, prime(n+j)), ", "))} \\ Klaus Brockhaus, Jan 21 2007

(PARI) {m=10; k=12; for(n=1, m, print1(polcoeff(prod(j=0, k-1, (x-prime(n+j))), 0), ", "))} \\ Klaus Brockhaus, Jan 21 2007

(Magma) [&*[ NthPrime(n+k): k in [0..11] ]: n in [1..50] ]; // Vincenzo Librandi, Apr 03 2011

CROSSREFS

Cf. A006094, A046301, A046302, A046303, A046324, A046325, A046326, A046327, A127342, A127343.

Sequence in context: A023051 A345865 A003826 * A186179 A058124 A282540

Adjacent sequences: A127341 A127342 A127343 * A127345 A127346 A127347

KEYWORD

nonn,changed

AUTHOR

Artur Jasinski, Jan 11 2007

EXTENSIONS

Edited by Klaus Brockhaus, Jan 21 2007

STATUS

approved