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 A319016 #20 Oct 01 2024 11:49:28
%S A319016 1,2,6,5,8,7,0,0,9,5,2,3,0,8,6,6,3,6,8,4,1,8,9,2,1,3,1,4,5,4,3,5,4,3,
%T A319016 4,2,7,4,6,4,2,6,5,4,4,6,3,9,9,6,3,8,7,1,6,8,2,0,0,5,3,3,4,1,8,1,4,8,
%U A319016 9,3,4,9,2,5,1,1,2,7,4,8,9,4,4,3,7,0,6,4,5,9,7,4,8,3,5,3,0,5,6,7,3,9,0,8,4,2,7,1,1,4
%N A319016 Decimal expansion of Sum_{k>=0} 1/2^(k*(k+1)).
%C A319016 The binary expansion is the characteristic function of the oblong numbers (A005369).
%C A319016 The Engel expansion of this constant are the powers of 4 (A000302). - _Amiram Eldar_, Dec 07 2020
%F A319016 Equals theta_2(1/2)/2^(3/4), where theta_2 is the Jacobi theta function.
%F A319016 Equals Product_{k>=1} (1 - 1/4^k)^((-1)^k). - _Antonio Graciá Llorente_, Oct 01 2024
%e A319016 1.2658700952308663684189... = (1.010001000001000000010000000001...)_2.
%e A319016 | | | | | |
%e A319016 0 2 6 12 20 30
%t A319016 RealDigits[EllipticTheta[2, 0, 1/2]/2^(3/4), 10, 110] [[1]]
%o A319016 (PARI) suminf(k=0, 1/2^(k*(k+1))) \\ _Michel Marcus_, Sep 08 2018
%Y A319016 Cf. A000302, A002378, A005369, A053763, A190405, A299998, A319015.
%K A319016 nonn,cons
%O A319016 1,2
%A A319016 _Ilya Gutkovskiy_, Sep 07 2018