cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A130506 #21 Sep 08 2022 08:45:30
%S A130506 1,2,42,24024,43609104000,1315041316842168115200000,
%T A130506 3529525662153455013215570189186777498682088488960000000
%N 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.
%C A130506 The first four terms agree with a Riemann Hypothesis related sequence.
%D A130506 Marcus du Sautoy, "The Music of the Primes", Harper Collins, 2003.
%H A130506 G. C. Greubel, <a href="/A130506/b130506.txt">Table of n, a(n) for n = 1..10</a>
%e A130506 a(4) = 24024 because 24024 = (16 - 5 + 0)*(16 - 5 + 1)*(16 - 5 + 2)*(16 - 5 + 3).
%t A130506 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 *)
%o A130506 (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
%o A130506 (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
%Y A130506 Cf. A039622.
%K A130506 easy,nonn
%O A130506 1,2
%A A130506 Ben de la Rosa & Johan Meyer (meyerjh.sci(AT)ufs.ac.za), Aug 08 2007
%E A130506 a(7) from _Robert G. Wilson v_, Oct 14 2012