A345202 Decimal expansion of gamma + zeta(2), where gamma is Euler's constant (A001620).

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

Offset

1,1

Comments

The value of the sum (see the Formula section) discovered in 1926 by the Italian mathematician and historian of science Giovanni Enrico Eugenio Vacca (1872-1953).

References

G. Vacca, Nuova serie per la costante di Eulero, C=0,577..., Rendiconti, Accademia Nazionale dei Lincei, Roma, Classe di Scienze Fisiche, Matematiche e Naturali, Serie 6, Vol. 3 (1926), pp. 19-20.

Links

Table of n, a(n) for n=1..87.

Ettore Carruccio, Giovanni Vacca, matematico, storico e filosofo della scienza, Bollettino dell'Unione Matematica Italiana, Serie 3, Vol. 8 (1953), pp. 448-456.

Tanguy Rivoal, Is Euler's constant a value of an arithmetic special function?, 2017.

Formula

Equals Sum_{k>=1} (1/floor(sqrt(k))^2 - 1/k) (Vacca, 1926).

Equals Sum_{k>=1} f(k)/k^2, where f(k) = Sum_{j=1..2*k} j/(j + k^2).

Equals A001620 + A013661.

Example

2.22214973174975929707892725672842762026110923714672...

Mathematica

RealDigits[EulerGamma + Pi^2/6, 10, 100][[1]]

Crossrefs

Cf. A001620, A013661, A048760.

Sequence in context: A276830 A064741 A281659 * A308619 A114294 A371929

Adjacent sequences: A345199 A345200 A345201 * A345203 A345204 A345205

Keyword

nonn,cons

Author

Amiram Eldar, Jun 10 2021

Status

approved