A127342 Product of 10 consecutive primes.

6469693230, 100280245065, 1236789689135, 10141675450907, 62298863484143, 266186053068611, 1085220062510491, 3766351981654057, 12091972151626183, 35224440615606707, 86239147714071593, 203079283326684719, 433601713048867373, 877779077635511999, 1816798556036292277

Offset

1,1

Comments

a(n) = coefficient of x^0 of the polynomial Product_{j=0..9} (x-prime(n+j)) of degree 10; the roots of this polynomial are prime(n), ..., prime(n+9).

Links

Table of n, a(n) for n=1..15.

Mathematica

a = {}; Do[AppendTo[a, Product[Prime[x + n], {n, 0, 9}]], {x, 1, 50}]; a
Times@@@Partition[Prime[Range[50]], 10, 1] (* Harvey P. Dale, Oct 21 2011 *)

Prog

(PARI) {m=12; k=10; for(n=0, m-1, print1(a=prod(j=1, k, prime(n+j)), ", "))} \\ Klaus Brockhaus, Jan 21 2007
(PARI) {m=12; k=10; 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..9] ]: n in [1..50] ]; // Vincenzo Librandi, Apr 03 2011

Crossrefs

Cf. A006094, A046301, A046302, A046303, A046324, A046325, A046326, A046327, A127343, A127344.

Sequence in context: A358489 A281222 A258365 * A336681 A391284 A268845

Adjacent sequences: A127339 A127340 A127341 * A127343 A127344 A127345

Keyword

nonn

Author

Artur Jasinski, Jan 11 2007

Extensions

Edited by Klaus Brockhaus, Jan 21 2007

More terms from Michel Marcus, Mar 16 2026

Status

approved