A082486 - OEIS

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A082486

Decimal expansion of the constant c satisfying Sum_{k>=1} 1/c^sqrtint(k) = 1 where sqrtint(k) = floor(sqrt(k)).

4, 5, 6, 1, 5, 5, 2, 8, 1, 2, 8, 0, 8, 8, 3, 0, 2, 7, 4, 9, 1, 0, 7, 0, 4, 9, 2, 7, 9, 8, 7, 0, 3, 8, 5, 1, 2, 5, 7, 3, 5, 9, 9, 6, 1, 2, 6, 8, 6, 8, 1, 0, 2, 1, 7, 1, 9, 9, 3, 1, 6, 7, 8, 6, 5, 4, 7, 4, 7, 7, 1, 7, 3, 1, 6, 8, 8, 1, 0, 7, 9, 6, 7, 9, 3, 9, 3, 1, 8, 2, 5, 4, 0, 5, 3, 4, 2, 1, 4, 8, 3, 4, 2, 2, 7

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

FORMULA

Equals 5/2 + sqrt(17)/2.

EXAMPLE

4.5615528128088302749107049....

Sum_{k=1..1000} 1/c^sqrtint(k) = 0.9999999999999999998470351081791855275...

MATHEMATICA

RealDigits[(5 + Sqrt[17])/2, 10, 100][[1]] (* Amiram Eldar, May 21 2022 *)