cp's OEIS Frontend

A127489 a(n) is the coefficient of the linear term in the polynomial (x-prime(n))*(x-prime(n+1))*(x-prime(n+2))*(x-prime(n+3))*(x-prime(n+4)).

%I A127489 #15 Apr 23 2023 14:38:19
%S A127489 2927,12673,48457,136489,342889,745945,1480489,2760049,5070049,
%T A127489 8292889,12185065,18656761,27138729,37294369,53106049,73698049,
%U A127489 95048089,120087129,153503149,192747937,247731385,321039529,396584569,485290729
%N A127489 a(n) is the coefficient of the linear term in the polynomial (x-prime(n))*(x-prime(n+1))*(x-prime(n+2))*(x-prime(n+3))*(x-prime(n+4)).
%C A127489 Arithmetic derivative (see A003415) of prime(n)*prime(n+1)*prime(n+2)*prime(n+3)*prime(n+4). [_Giorgio Balzarotti_, May 26 2011]
%e A127489 a(1) is the coefficient of the linear term of (x-2)*(x-3)*(x-5)*(x-7)*(x-11).
%e A127489 This polynomial is -2310 + 2927*x - 1358*x^2 + 288*x^3 - 28*x^4 + x^5, the coefficient of the linear term equals 2927; hence a(1) = 2927.
%p A127489 A127489 := proc(n)
%p A127489     local x,j ;
%p A127489     mul( x-ithprime(n+j),j=0..4) ;
%p A127489     expand(%) ;
%p A127489     coeff(%,x,1) ;
%p A127489 end proc:
%p A127489 seq(A127489(n),n=1..60) ; # _R. J. Mathar_, Apr 23 2023
%t A127489 Table[CoefficientList[Expand[(x-Prime[n])*(x-Prime[n+1])*(x-Prime[n+2])* (x-Prime[n+3])*(x-Prime[n+4])],x][[2]],{n,1,24}]
%Y A127489 Cf. A127490.
%K A127489 nonn,less
%O A127489 1,1
%A A127489 _Artur Jasinski_, Jan 16 2007
%E A127489 Edited by _Stefan Steinerberger_, Jul 18 2007