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

1,2

Comments

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

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A039622.

Sequence in context: A182192 A330229 A039622 * A273399 A052078 A069544

Adjacent sequences: A130503 A130504 A130505 * A130507 A130508 A130509

Keyword

easy,nonn

Author

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

Extensions

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

Status

approved