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

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, 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, 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

Offset: 0

Author

Jean-François Alcover, Apr 18 2016

Keywords

• nonn
• cons

Comments

This constant is an analog of A084256 where primes are replaced with squares.

Examples

			0.705346681379806989636379706393941505260078161512292870517426781...
		

Links

• Eric Weisstein's MathWorld, Jacobi Theta Functions

Crossrefs

Cf. A000122, A084256.

Programs

Mathematica

FindRoot[Sum[x^n^2, {n, 1, 100}] == 1, {x, 7/10}, WorkingPrecision -> 100][[1, 2]] // RealDigits // First
(* or *)
FindRoot[EllipticTheta[3, 0, x] == 3, {x, 7/10}, WorkingPrecision -> 100][[1, 2]] // RealDigits // First

PARI

solve(x=.7,.8,suminf(y=1,x^y^2)-1) \\ Charles R Greathouse IV, Apr 25 2016

Formula

Solution to theta_3(0,x) = 3, where theta_3 is the 3rd elliptic theta function.

Extensions

a(99) corrected by Sean A. Irvine, Jul 24 2025