cp's OEIS Frontend

A074638 Denominator of 1/3 + 1/7 + 1/11 + ... + 1/(4n-1).

%I A074638 #30 Aug 14 2023 08:32:01
%S A074638 3,21,231,385,7315,168245,4542615,140821065,28164213,366134769,
%T A074638 15743795067,739958368149,12579292258533,62896461292665,
%U A074638 3710891216267235,3710891216267235,248629711489904745,17652709515783236895,88263547578916184475,6972820258734378573525
%N A074638 Denominator of 1/3 + 1/7 + 1/11 + ... + 1/(4n-1).
%C A074638 This s(n) := Sum_{j=0..n-1} 1/(4*j + 3), for n >= 1, equals (Psi(n + 3/4) - Psi(3/4))/4, with the digamma function Psi(z). See Abramowitz-Stegun, p. 258, eqs. 6.3.7 and 6.3.5, with z -> 3/4. A200134 = -Psi(3/4). - _Wolfdieter Lang_, Apr 06 2022
%H A074638 Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP?Res=150&amp;Page=258">Handbook of Mathematical Functions. p.258</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. p. 258.
%F A074638 Denominator( (Psi(n + 3/4) - Psi(3/4))/4 ). See the comment above. - _Wolfdieter Lang_, Apr 05 2022
%t A074638 Table[ Denominator[ Sum[1/i, {i, 3/4, n}]], {n, 1, 20}]
%o A074638 (Python)
%o A074638 from fractions import Fraction
%o A074638 def a(n): return sum(Fraction(1, 4*i-1) for i in range(1, n+1)).denominator
%o A074638 print([a(n) for n in range(1, 21)]) # _Michael S. Branicky_, Mar 21 2021
%o A074638 (PARI) a(n) = denominator(sum(i=1, n, 1/(4*i-1))); \\ _Michel Marcus_, Mar 21 2021
%Y A074638 The numerators times 4 are A074637.
%Y A074638 Cf. A075135, A200134.
%K A074638 easy,frac,nonn
%O A074638 1,1
%A A074638 _Robert G. Wilson v_, Aug 27 2002