cp's OEIS Frontend

A136370 Numerator of 1 - Sum_{k=1..n} (-1)^(k+1)/prime(k)^2.

%I A136370 #31 Jun 26 2022 14:03:43
%S A136370 3,31,739,37111,4446331,756766039,217803584371,78887714418031,
%T A136370 41637516941042299,35066922176061410359,33657455280704707522099,
%U A136370 46117280789485930425170431,77468081652660425646977758411,143331051198625503752852285686039
%N A136370 Numerator of 1 - Sum_{k=1..n} (-1)^(k+1)/prime(k)^2.
%C A136370 It seems that the denominator of 1 - Sum_{k=1..n} (-1)^(k+1)/prime(k)^2 is A061742(n), which is the square of the product of the first n primes, but this is not immediately obvious. - _Petros Hadjicostas_, May 14 2020
%H A136370 Michael S. Branicky, <a href="/A136370/b136370.txt">Table of n, a(n) for n = 1..195</a>
%F A136370 A136370/A061742 tends to 1 - A242301 = 0.83718375333639858423166... - _Vaclav Kotesovec_, May 14 2020
%e A136370 The first few fractions are 3/4, 31/36, 739/900, 37111/44100, 4446331/5336100, 756766039/901800900, ... = A136370/A061742. - _Petros Hadjicostas_, May 14 2020
%t A136370 Table[Numerator[1 - Sum[(-1)^(k+1)/Prime[k]^2, {k, 1, n}]], {n, 1, 20}]
%o A136370 (PARI) a(n) = numerator(1 - sum(k=1, n, (-1)^(k+1)/prime(k)^2)); \\ _Michel Marcus_, May 14 2020
%o A136370 (Python)
%o A136370 from sympy import prime
%o A136370 from fractions import Fraction
%o A136370 from itertools import accumulate, count, islice
%o A136370 def A136370gen(): yield from map(lambda x: (1-x).numerator, accumulate(Fraction((-1)**(k+1), prime(k)**2) for k in count(1)))
%o A136370 print(list(islice(A136370gen(), 14))) # _Michael S. Branicky_, Jun 26 2022
%Y A136370 Possible denominators are A061742.
%Y A136370 Cf. A024530, A136365, A136366, A136367, A136368, A136369, A136371.
%K A136370 nonn,frac
%O A136370 1,1
%A A136370 _Alexander Adamchuk_, Dec 27 2007
%E A136370 Definition corrected by _Alexander Adamchuk_, Sep 15 2010
%E A136370 a(14) and beyond from _Michael S. Branicky_, Jun 26 2022