cp's OEIS Frontend

A272037 Decimal expansion of x such that x + x^4 + x^9 + x^16 + x^25 + x^36 + ... = 1.

%I A272037 #16 Jul 24 2025 04:03:36
%S A272037 7,0,5,3,4,6,6,8,1,3,7,9,8,0,6,9,8,9,6,3,6,3,7,9,7,0,6,3,9,3,9,4,1,5,
%T A272037 0,5,2,6,0,0,7,8,1,6,1,5,1,2,2,9,2,8,7,0,5,1,7,4,2,6,7,8,1,6,2,7,3,8,
%U A272037 1,2,3,3,5,0,6,2,0,9,5,1,4,6,2,1,3,7,4,7,1,9,4,8,3,8,8,1,2,2,1,0
%N A272037 Decimal expansion of x such that x + x^4 + x^9 + x^16 + x^25 + x^36 + ... = 1.
%C A272037 This constant is an analog of A084256 where primes are replaced with squares.
%H A272037 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>
%F A272037 Solution to theta_3(0,x) = 3, where theta_3 is the 3rd elliptic theta function.
%e A272037 0.705346681379806989636379706393941505260078161512292870517426781...
%t A272037 FindRoot[Sum[x^n^2, {n, 1, 100}] == 1, {x, 7/10}, WorkingPrecision -> 100][[1, 2]] // RealDigits // First
%t A272037 (* or *)
%t A272037 FindRoot[EllipticTheta[3, 0, x] == 3, {x, 7/10}, WorkingPrecision -> 100][[1, 2]] // RealDigits // First
%o A272037 (PARI) solve(x=.7,.8,suminf(y=1,x^y^2)-1) \\ _Charles R Greathouse IV_, Apr 25 2016
%Y A272037 Cf. A000122, A084256.
%K A272037 nonn,cons
%O A272037 0,1
%A A272037 _Jean-François Alcover_, Apr 18 2016
%E A272037 a(99) corrected by _Sean A. Irvine_, Jul 24 2025