A130506 a(1)=1; a(n) = Product_{r=0..2^(n-2)-1} (n^2 - prime(n-1) + r) if n > 1, where prime(i) is the i-th prime.

1, 2, 42, 24024, 43609104000, 1315041316842168115200000, 3529525662153455013215570189186777498682088488960000000

Offset: 1

Author

Ben de la Rosa & Johan Meyer (meyerjh.sci(AT)ufs.ac.za), Aug 08 2007

Keywords

• easy
• nonn

Comments

The first four terms agree with a Riemann Hypothesis related sequence.

Examples

			a(4) = 24024 because 24024 = (16 - 5 + 0)*(16 - 5 + 1)*(16 - 5 + 2)*(16 - 5 + 3).
		

References

• Marcus du Sautoy, "The Music of the Primes", Harper Collins, 2003.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10

Crossrefs

Cf. A039622.

Programs

Magma

[1] cat [(&*[ n^2 -NthPrime(n-1) +j: j in [0..(2^(n-2)-1)]]): n in [2..10]]; // G. C. Greubel, May 04 2021

Mathematica

f[n_]:= Product[n^2 - Prime[n-1] + i, {i, 0, 2^(n-2) -1}]; f[1] = 1; Array[f, 7] (* Robert G. Wilson v, Oct 14 2012 *)

Sage

[1]+[product( n^2 -nth_prime(n-1) +j for j in (0..(2^(n-2)-1)) ) for n in (2..10)] # G. C. Greubel, May 04 2021

Extensions

a(7) from Robert G. Wilson v, Oct 14 2012