Magata,s Constant
المؤلف:
Sloane, N. J. A.
المصدر:
Sequences A092894, A118203, A118204, A118210, and A118210 in "The On-Line Encyclopedia of Integer Sequences."
الجزء والصفحة:
...
17-3-2020
1439
Magata,s Constant
Consider the Lagrange interpolating polynomial
 |
(1)
|
through the points 
, where 
is the 
th prime. For the first few points, the polynomials are
So the first few values of 
, 
, 
, ..., are 2, 1, 1/2, 
, 1/8, 
, ... (OEIS A118210 and A118211).
Now consider the partial sums of these coefficients, namely 2, 3, 7/2, 10/3, 83/24, 203/60, 2459/720, ... (OEIS A118203 and A118204). As first noted by F. Magata in 1998, the sum appears to converge to the value 3.407069... (OEIS A092894), now known as Magata's constant.
REFERENCES:
Sloane, N. J. A. Sequences A092894, A118203, A118204, A118210, and A118210 in "The On-Line Encyclopedia of Integer Sequences."
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