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 A275975 #41 Jun 11 2023 02:54:29
%S A275975 3,0,8,6,0,9,0,0,8,5,5,6,2,3,1,8,5,6,4,0,0,3,4,0,4,7,9,7,1,8,0,2,5,2,
%T A275975 2,1,6,9,7,4,3,3,9,0,4,1,6,6,4,4,1,3,6,6,8,0,1,3,6,7,2,2,1,1,5,6,9,4,
%U A275975 4,3,8,5,8,0,5,4,6,1,9,7,2,2,7,6,6,2,4,8,7,5,6,4,0,8,5,3,5,0,7,0,8,6,1,6,6
%N A275975 Decimal expansion of Sum_{k>=0}((-1)^k/2^(2^k)).
%C A275975 Except for the alternating signs, this constant is defined in a similar way to the Kempner-Mahler number A007404. It is related to the Jeffreys binary sequence A275973 somewhat like Kempner-Mahler number is related to the Fredholm-Rueppel sequence A036987.
%C A275975 Conjecture: Numbers of the type Sum_{k>=0}(x^(2^k)) with algebraic x and |x|<1 are known to be transcendental (Mahler 1930, Adamczewski 2013). It is likely that the alternating sign does not invalidate this property.
%C A275975 Yes, this number is transcendental. It is among various such forms Kempner showed are transcendental. - _Kevin Ryde_, Jul 12 2019
%H A275975 Boris Adamczewski, <a href="https://arxiv.org/abs/1303.1685">The Many Faces of the Kempner Number</a>, arXiv:1303.1685 [math.NT], 2013.
%H A275975 Aubrey J. Kempner, <a href="http://www.jstor.org/stable/1988833">On Transcendental Numbers</a>, Transactions of the American Mathematical Society 17 (1916), pp. 476-482.
%H A275975 Kurt Mahler, <a href="http://dx.doi.org/10.1007/BF01194652">Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen</a>, Math. Z. 32 (1930), 545-585.
%H A275975 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A275975 0.308609008556231856400340479718025221697433904166441366801367221...
%t A275975 RealDigits[N[Sum[((-1)^k/2^(2^k)), {k, 0, Infinity}], 120]][[1]] (* _Amiram Eldar_, Jun 11 2023 *)
%o A275975 (PARI) default(realprecision,2100);suminf(k=0,(-1)^k*0.5^2^k)
%Y A275975 Cf. A030300 (binary expansion), A160386.
%Y A275975 Cf. A007404, A036987, A275973.
%K A275975 nonn,cons
%O A275975 0,1
%A A275975 _Stanislav Sykora_, Aug 15 2016