cp's OEIS Frontend

A101464 Decimal expansion of sqrt(2-sqrt(2)), edge length of a regular octagon with circumradius 1.

%I A101464 #46 Feb 16 2025 08:32:55
%S A101464 7,6,5,3,6,6,8,6,4,7,3,0,1,7,9,5,4,3,4,5,6,9,1,9,9,6,8,0,6,0,7,9,7,7,
%T A101464 3,3,5,2,2,6,8,9,1,2,4,9,7,1,2,5,4,0,8,2,8,6,7,6,0,1,2,7,1,2,5,5,0,9,
%U A101464 2,0,6,7,9,2,0,1,7,9,3,8,4,4,7,4,0,2,7,5,7,0,6,8,4,5,6,7,0,9,4,2,9,6,8,4,8
%N A101464 Decimal expansion of sqrt(2-sqrt(2)), edge length of a regular octagon with circumradius 1.
%H A101464 G. C. Greubel, <a href="/A101464/b101464.txt">Table of n, a(n) for n = 0..5000</a>
%H A101464 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Octagon.html">Octagon</a>.
%H A101464 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F A101464 Equals i^(3/4) + i^(-3/4). - _Gary W. Adamson_, Jul 07 2022
%F A101464 Equals 2*sin(Pi/8) = 2*A182168. - _Amiram Eldar_, Apr 06 2023
%F A101464 Equals Product_ {k >= 0} ((8*k - 2)*(8*k + 10))/((8*k - 5)*(8*k + 13)). - _Antonio Graciá Llorente_, Mar 11 2024
%F A101464 Equals Product_{k>=1} (1 + (-1)^k/A047621(k)). - _Amiram Eldar_, Nov 22 2024
%F A101464 Equals sqrt(A101465) = 1/A285871 = exp(-A329246). - _Hugo Pfoertner_, Nov 22 2024
%e A101464 0.765366864730179543456919968060797733522689124971254082867601271255092067920...
%t A101464 RealDigits[Sqrt[2-Sqrt[2]],10,120][[1]] (* _Harvey P. Dale_, Jun 22 2011 *)
%o A101464 (PARI) 2*sin(Pi/8) \\ _Charles R Greathouse IV_, Feb 04 2025
%o A101464 (PARI) polrootsreal(x^4-4*x^2+2)[3] \\ _Charles R Greathouse IV_, Feb 04 2025
%Y A101464 Cf. A047621, A101465, A179260 (sqrt(2+sqrt(2))), A182168, A285871, A329246.
%K A101464 cons,nonn
%O A101464 0,1
%A A101464 Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jan 20 2005