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.
%I A061642 #41 Feb 16 2025 08:32:44
%S A061642 4,1,5,1,1,8,0,8,6,3,2,3,7,4,1,5,7,5,7,1,6,5,2,8,5,5,6,1,9,5,9,5,3,7,
%T A061642 5,1,5,7,9,9,4,1,0,0,1,9,3,3,3,9,6,3,0,3,2,0,2,7,1,6,3,3,4,9,5,2,1,9,
%U A061642 9,8,3,5,8,5,0,5,3,5,5,4,2,9,9,8,6,8,4,3,5,7,3,2,0,3,1,5,1,6,6,8,3,3,4,0,6
%N A061642 Decimal expansion of Hardy-Littlewood constant for prime quadruples.
%C A061642 Computed by Robert Harley.
%D A061642 Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 84-94.
%H A061642 Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/hrdyltl/hrdyltl.html">Hardy-Littlewood Constants</a>. [Broken link]
%H A061642 Steven R. Finch, <a href="http://web.archive.org/web/20010614100031/http://www.mathsoft.com/asolve/constant/hrdyltl/hrdyltl.html">Hardy-Littlewood Constants</a>. [From the Wayback machine]
%H A061642 Warut Roonguthai, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;a9e07686.9609">Large Prime Quadruplets</a>, NMBRTHRY Archives.
%H A061642 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeQuadruplet.html">Prime Quadruplet</a>.
%F A061642 Equals (27/2) * Product_{p prime > 3} (p^3)*(p-4)/((p-1)^4) using 27/2 = (3*(11+13)+(17+19))/4. - _Frank Ellermann_, Mar 31 2020
%e A061642 4.151180863237415757165285561959537515799410019333963032027163...
%t A061642 $MaxExtraPrecision = 1500; digits = 105; terms = 1500; P[n_] := PrimeZetaP[n] - 1/2^n - 1/3^n; LR = Join[{0, 0}, LinearRecurrence[{5, -4}, {-12, -60}, terms + 10]]; r[n_Integer] := LR[[n]]; (27/2)* Exp[NSum[ r[n]*P[n-1]/(n-1), {n, 3, terms}, NSumTerms -> terms,WorkingPrecision -> digits + 10]] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Apr 16 2016 *)
%o A061642 (PARI) (27/2) * prodeulerrat((p^3)*(p-4)/((p-1)^4), 1, 5) \\ _Amiram Eldar_, Mar 12 2021
%Y A061642 Cf. A065419 (constant without factor 27/2), A333586, A333587.
%K A061642 cons,nonn
%O A061642 1,1
%A A061642 _Jason Earls_, Jun 13 2001