|
|
A272037
|
|
Decimal expansion of x such that x + x^4 + x^9 + x^16 + x^25 + x^36 + ... = 1.
|
|
0
|
|
|
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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
This constant is an analog of A084256 where primes are replaced with squares.
|
|
LINKS
|
|
|
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
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|