A360510 a(n) = Product_{i=2..n} p(i) - p(n+1)^2, where p(i) is the i-th prime.

-8, -22, -34, -16, 986, 14726, 254894, 4849316, 111545594, 3234845654, 100280243696, 3710369065724, 152125131761756, 6541380665832806, 307444891294242896, 16294579238595018884, 961380175077106315814, 58644190679703485487146, 3929160775540133527934504, 278970415063349480483702366

Offset: 1

Author

N. J. A. Sloane, Feb 24 2023

Keywords

• sign

Comments

It is known that a(n) >= 0 for n >= 5.

Remember an empty product equals 1 by convention.

See A064819 for another version.

References

• S. W. Golomb, Elementary Problem E3137, Amer. Math. Monthly, Proposed 93 (1986), p. 215; Solution and Editorial Comments, 94 (1987), 883-884.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A062234, A064819, A360511.

Programs

Mathematica

FoldList[Times, 1, Most[#]] - #^2 & [Prime[Range[2, 25]]] (* Paolo Xausa, Nov 06 2024 *)

Python

from sympy import prime, primorial
def A360510(n): return (primorial(n)>>1)-prime(n+1)**2 # Chai Wah Wu, Feb 24 2023