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%I #15 Sep 08 2022 08:45:29
%S 6469693230,100280245065,1236789689135,10141675450907,62298863484143,
%T 266186053068611,1085220062510491,3766351981654057,12091972151626183,
%U 35224440615606707,86239147714071593,203079283326684719
%N Product of 10 consecutive primes.
%C 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).
%t a = {}; Do[AppendTo[a, Product[Prime[x + n], {n, 0, 9}]], {x, 1, 50}]; a
%t Times@@@Partition[Prime[Range[50]],10,1] (* _Harvey P. Dale_, Oct 21 2011 *)
%o (PARI) 1. {m=12;k=10;for(n=0,m-1,print1(a=prod(j=1,k,prime(n+j)),","))} 2. {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
%o (Magma) [&*[ NthPrime(n+k): k in [0..9] ]: n in [1..50] ]; // _Vincenzo Librandi_, Apr 03 2011
%Y Cf. A006094, A046301, A046302, A046303, A046324, A046325, A046326, A046327, A127343, A127344.
%K nonn
%O 1,1
%A _Artur Jasinski_, Jan 11 2007
%E Edited by _Klaus Brockhaus_, Jan 21 2007
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