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 A104225 #37 May 24 2025 16:19:33
%S A104225 6,6,5,0,7,0,0,4,8,7,6,4,8,5,2,2,9,2,0,4,3,4,8,7,1,4,3,2,8,0,8,7,1,4,
%T A104225 5,8,9,4,2,2,8,1,0,5,2,6,1,3,6,4,6,0,6,0,4,2,4,0,2,8,5,9,0,6,0,9,4,1,
%U A104225 2,3,4,0,3,7,0,7,2,8,4,1,9,5,9,0,0,9,1,0,1,5,6,4,6,4,0,0,6,4,9,8
%N A104225 Decimal expansion of -x, where x is the real root of f(x) = 1 + Sum_{n} (twin_prime(n))*x^n.
%D A104225 S. R. Finch, "Kalmar's Composition Constant", Section 5.5 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 292-295, 2003.
%D A104225 Martin Gardner, "Patterns in Primes are a Clue to the Strong Law of Small Numbers." Sci. Amer. 243, 18-28, Dec. 1980.
%D A104225 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, 1979.
%H A104225 S. R. Finch, <a href="/A104225/a104225.pdf">Backhouse's constant</a>. 1995 [Cached copy, with permission]
%H A104225 Philippe Flajolet, in response to the previous document from S. R. Finch, <a href="/A104225/a104225.txt">Backhouse's constant</a>, 1995
%H A104225 S. R. Finch, <a href="/A104225/a104225_1.pdf">Kalmar's Composition Constant</a>, Section 5.5 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 292-295, 2003. [Cached copy, with permission]
%H A104225 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BackhousesConstant.html">Backhouse's Constant.</a>
%H A104225 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes.</a>
%F A104225 Decimal expansion of -x where x is the real root of f(x) = 1 + 3x + 5x^2 + 5x^3 + 7x^4 + 11x^5 + 13x^6 + 17x^7 + 19x^8 + 29x^9 + 31x^10 + 41x^11 + 43x^12 + 59x^13 + 61x^14 + 71x^15 + 73x^16 + ... where for n>0 the coefficient of x^n is the n-th twin prime.
%e A104225 -0.665070048764852292...
%t A104225 ps={}; Do[If[PrimeQ[n]&&PrimeQ[n+2], AppendTo[ps, {n, n+2}]], {n, 3, 40001, 2}];
%t A104225 ps=Flatten[ps];
%t A104225 RealDigits[ -x /. FindRoot[0==1+Sum[x^n ps[[n]], {n, 1000}], {x, -0.665}, WorkingPrecision->100]][[1]] (* _T. D. Noe_ *)
%Y A104225 Cf. A072508, A074269, A077800, A088751.
%K A104225 cons,nonn
%O A104225 0,1
%A A104225 _Jonathan Vos Post_, Apr 01 2005
%E A104225 Offset corrected by _Sean A. Irvine_, May 24 2025
%E A104225 a(99) corrected by _Michael De Vlieger_, May 24 2025