A359106 Decimal expansion of Integral_{x=0..1} ([1/x]^(-1) + {1/x}) dx, where [x] denotes the integer part of x and {x} the fractional part of x.

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

Offset

1,3

Links

Table of n, a(n) for n=1..95.

Vincent Pantaloni, Solution to Problem #133, Missouri State University's Advanced Problem of February 2010.

Michael I. Shamos, Shamos's Catalog of the Real Numbers, 2007, p. 105.

Formula

Equals Pi^2/6 - gamma.

Equals zeta(2) - gamma.

Equals A013661 - A001620.

From Amiram Eldar, Apr 11 2026: (Start)

Formulas from Shamos (2007):

Equals Sum_{k>=1} k^2*(zeta(k+1)-1)/(k+1).

Equals Sum_{k>=1} psi(k+1)/(k*(k+1)), where psi is the digamma function. (End)

Example

1.06771840194669357586590307656362275817679...

Maple

Digits := 110: evalf(Pi^2/6 - gamma, Digits)*10^94:
ListTools:-Reverse(convert(floor(%), base, 10));

Mathematica

RealDigits[Zeta[2] - EulerGamma, 10, 120][[1]] (* Amiram Eldar, Apr 11 2026 *)

Prog

(PARI) zeta(2) - Euler \\ Amiram Eldar, Apr 11 2026

Crossrefs

Cf. A013661, A001620.

Sequence in context: A249539 A139726 A200095 * A201753 A084256 A391815

Adjacent sequences: A359103 A359104 A359105 * A359107 A359108 A359109

Keyword

nonn,cons

Author

Peter Luschny, Dec 16 2022

Status

approved