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Product of next n primes.
(Formerly M2085)
3

%I M2085 #33 Feb 15 2021 16:03:47

%S 2,15,1001,215441,95041567,66238993967,63009974049301,

%T 87796770491685553,173955570033393401009,421385360593324054690769,

%U 1172248885422611971256631487,5253333091597988325086927419397,21476254926032216698855019795863013

%N Product of next n primes.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Harvey P. Dale, <a href="/A007467/b007467.txt">Table of n, a(n) for n = 1..185</a>

%H Ronald K. Hoeflin, <a href="https://web.archive.org/web/20080731175458/http://www.eskimo.com/~miyaguch/titan.html">Titan Test</a>.

%F From _Amiram Eldar_, Nov 15 2020: (Start)

%F Sum_{n>=1} 1/a(n) = A139395.

%F Sum_{n>=1} (-1)^(n+1)/a(n) = A238234 = 1 - A139396. (End)

%t terms=20;With[{prs=Prime[Range[(terms(terms+1))/2]]},Table[ Times@@ Take[prs,{(n(n-1))/2+1,(n(n+1))/2}],{n,terms}]] (* _Harvey P. Dale_, Aug 06 2013 *)

%t With[{nn=40},Times@@@TakeList[Prime[Range[(nn(nn+1))/2]],Range[nn]]] (* Requires Mathematica version 11 or later *) (* _Harvey P. Dale_, Jan 15 2020 *)

%o (PARI) a(n)=my(s=1);forprime(p=prime(n*(n-1)/2+1),prime(n*(n+1)/2),s*=p);s \\ _Charles R Greathouse IV_, Aug 06 2013

%o (Python)

%o from math import prod

%o from sympy import prime

%o def a(n): return prod(prime(i) for i in range((n-1)*n//2+1, n*(n+1)//2+1))

%o print([a(n) for n in range(1, 14)]) # _Michael S. Branicky_, Feb 15 2021

%Y Cf. A139395, A139396, A238234.

%K easy,nonn

%O 1,1

%A _N. J. A. Sloane_, _Simon Plouffe_

%E Corrected and extended by _Harvey P. Dale_, Aug 06 2013