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.

A215085 a(n) = (A214089(n)^2 - 1) divided by four times the product of the first n primes.

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%I A215085 #40 Jul 14 2024 08:42:50
%S A215085 1,1,1,1,19,17,1,2567,3350,128928,3706896,1290179,100170428,39080794,
%T A215085 61998759572,7833495265,45119290746,581075656330,8672770990,
%U A215085 15792702394898740,594681417768520250,25509154378676494,1642780344643617537867,480931910076867717575
%N A215085 a(n) = (A214089(n)^2 - 1) divided by four times the product of the first n primes.
%C A215085 When floor(A214089(n) / 2) = A118478(n), a(n) = A215021(n).
%H A215085 J. Stauduhar, <a href="/A215085/b215085.txt">Table of n, a(n) for n = 1..30</a>
%F A215085 a(n) = (A214089(n)^2 - 1) / (4 * A002110(n)).
%e A215085 A214089(14) = 1430083494841, n#_14 = 13082761331670030, and (1430083494841^2 - 1) / (4 * 13082761331670030) = 39080794, so a(14) = 39080794.
%p A215085 A215085 := proc(n)
%p A215085         (A214089(n)^2-1)/4/A002110(n) ;
%p A215085 end proc: # _R. J. Mathar_, Aug 21 2012
%o A215085 (Python)
%o A215085 from itertools import product
%o A215085 from sympy import sieve, prime, isprime, primorial
%o A215085 from sympy.ntheory.modular import crt
%o A215085 def A215085(n):
%o A215085     return (
%o A215085         1
%o A215085         if n == 1
%o A215085         else (
%o A215085             int(
%o A215085                 min(
%o A215085                     filter(
%o A215085                         isprime,
%o A215085                         (
%o A215085                             crt(tuple(sieve.primerange(prime(n) + 1)), t)[0]
%o A215085                             for t in product((1, -1), repeat=n)
%o A215085                         ),
%o A215085                     )
%o A215085                 )
%o A215085             )
%o A215085             ** 2
%o A215085             - 1
%o A215085         )
%o A215085         // 4
%o A215085         // primorial(n)
%o A215085     )  # _Chai Wah Wu_, May 31 2022
%o A215085 for n in range(1, 16):
%o A215085     print(A215085(n), end=", ")
%K A215085 nonn
%O A215085 1,5
%A A215085 _J. Stauduhar_, Aug 02 2012