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Ramanujan's constant
From OeisWiki
Ramanujan's constant is^{[1]}
e π 
Ramanujan's constant is amazingly close to an integer, the first
12 
9 
Contents
Decimal expansion of Ramanujan's constant
The decimal expansion of Ramanujan's constant is (this is almost an integer!)
e π √ 163 

{2, 6, 2, 5, 3, 7, 4, 1, 2, 6, 4, 0, 7, 6, 8, 7, 4, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 5, 0, 0, 7, 2, 5, 9, 7, 1, 9, 8, 1, 8, 5, 6, 8, 8, 8, 7, 9, 3, 5, 3, 8, 5, 6, 3, 3, 7, 3, 3, 6, 9, 9, 0, 8, 6, 2, 7, 0, 7, 5, 3, 7, 4, 1, 0, ...}
Decimal expansion of a close approximation to Ramanujan's constant
Ramanujan's constant can be approximated to14 
24 
A102912 Decimal expansion of a close approximation to the Ramanujan constant.

{2, 6, 2, 5, 3, 7, 4, 1, 2, 6, 4, 0, 7, 6, 8, 7, 4, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 5, 1, 1, 2, 3, 8, 7, 5, 9, 3, 6, 7, 9, 9, 8, 0, 0, 9, 5, 4, 4, 1, 7, 3, 6, 7, 9, 1, 0, 2, 2, 7, 7, 1, 6, 6, 3, 5, 3, 5, 7, 0, 9, 1, 7, 6, 1, ...}
Continued fraction for Ramanujan's constant
The simple continued fraction for Ramanujan's constant is
e π √ 163 

{262537412640768743, 1, 1333462407511, 1, 8, 1, 1, 5, 1, 4, 1, 7, 1, 1, 1, 9, 1, 1, 2, 12, 4, 1, 15, 4, 299, 3, 5, 1, 4, 5, 5, 1, 28, 3, 1, 9, 4, 1, 6, 1, 1, 1, 1, 1, 1, 51, 11, 5, 3, 2, 1, 1, 1, 1, 2, 1, 5, 1, 9, 1, ...}
Sequences
A019297 Integers that are very close to values ofe π √ n 

{–1, 1, 2198, 422151, 614552, 2508952, 6635624, 199148648, 884736744, 24591257752, 30197683487, 147197952744, 545518122090, 70292286279654, 39660184000219160, 45116546012289600, ...}
n 
e π √ n 

{–1, 0, 6, 17, 18, 22, 25, 37, 43, 58, 59, 67, 74, 103, 148, 149, 163, 164, 177, 205, 223, 226, 232, 267, 268, 326, 359, 386, 522, 566, 630, 638, 652, 719, 790, 792, 928, 940, 986, 1005, 1014, 1169, 1194, ...}
−1 
n = −1 
e, π, i, 0, 
1 
1 
n = 0 
A178449 Conjectured expansion of
e π √ 163 
t 
t = 640320 − 3 

{1, 744, –196884, 167975456, –180592706130, 217940004309743, –19517553165954887, 74085136650518742, –131326907606533204, ...}
See also
Notes
 ↑ Interestingly,
is the largest Heegner number!−163  ↑ Weisstein, Eric W., Polynomial Roots, from MathWorld—A Wolfram Web Resource. [http://mathworld.wolfram.com/PolynomialRoots.html].