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, 1

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..99.

Eric Weisstein's MathWorld, Jacobi Theta Functions

Formula

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

Example

0.705346681379806989636379706393941505260078161512292870517426781...

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

Prog

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

Crossrefs

Cf. A000122, A084256.

Sequence in context: A116198 A137915 A316167 * A309724 A198114 A293384

Adjacent sequences: A272034 A272035 A272036 * A272038 A272039 A272040

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 18 2016

Status

approved