Consider the Lagrange interpolating polynomial
(1)
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through the points , where is the th prime. For the first few points, the polynomials are
(2)
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(3)
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(4)
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(5)
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(6)
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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.