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)).

2927, 12673, 48457, 136489, 342889, 745945, 1480489, 2760049, 5070049, 8292889, 12185065, 18656761, 27138729, 37294369, 53106049, 73698049, 95048089, 120087129, 153503149, 192747937, 247731385, 321039529, 396584569, 485290729

Offset: 1

Author

Artur Jasinski, Jan 16 2007

Keywords

• nonn
• less

Comments

Arithmetic derivative (see A003415) of prime(n)*prime(n+1)*prime(n+2)*prime(n+3)*prime(n+4). [Giorgio Balzarotti, May 26 2011]

Examples

			a(1) is the coefficient of the linear term of (x-2)*(x-3)*(x-5)*(x-7)*(x-11).
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.
		

Crossrefs

Cf. A127490.

Programs

Maple

A127489 := proc(n)
    local x,j ;
    mul( x-ithprime(n+j),j=0..4) ;
    expand(%) ;
    coeff(%,x,1) ;
end proc:
seq(A127489(n),n=1..60) ; # R. J. Mathar, Apr 23 2023

Mathematica

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}]

Extensions

Edited by Stefan Steinerberger, Jul 18 2007