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 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)). 7
 2927, 12673, 48457, 136489, 342889, 745945, 1480489, 2760049, 5070049, 8292889, 12185065, 18656761, 27138729, 37294369, 53106049, 73698049, 95048089, 120087129, 153503149, 192747937, 247731385, 321039529, 396584569, 485290729 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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] LINKS Table of n, a(n) for n=1..24. EXAMPLE 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. 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}] CROSSREFS Cf. A127490. Sequence in context: A180651 A180331 A043444 * A054831 A127490 A237079 Adjacent sequences: A127486 A127487 A127488 * A127490 A127491 A127492 KEYWORD nonn,less AUTHOR Artur Jasinski, Jan 16 2007 EXTENSIONS Edited by Stefan Steinerberger, Jul 18 2007 STATUS approved

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Last modified September 7 17:00 EDT 2024. Contains 375749 sequences. (Running on oeis4.)