A358646 Decimal expansion of 3/4 + log(4).

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

Offset

1,1

Links

Jason Bard, Table of n, a(n) for n = 1..10000

Joerg Bruedern and Trevor D. Wooley, Partitio Numerorum: sums of a prime and a number of k-th powers, arXiv:2211.10387 [math.NT], 2022, see p. 15.

Index entries for transcendental numbers.

Formula

Equals 2 + Integral_{x=0..1} (1 + x)*log(1 + x) - x dx. - Kritsada Moomuang, May 23 2025

Equals 2 + Sum_{k>=2} (-1)^k/(k*(k+1)*(k-1)). - Davide Rotondo, May 24 2025

Equals Integral_{x=1..2} 2/x + x/2 dx = 3/2 + Integral_{x=1..2} 2/x - x/2 dx. - Jason Bard, Jun 29 2025

Example

2.13629436111989061883446424291635313615100026872051050824136...

Mathematica

First[RealDigits[N[3/4+Log[4], 90]]]

Crossrefs

Cf. A016627, A358645.

Sequence in context: A238960 A238973 A335444 * A006895 A202204 A289815

Adjacent sequences: A358643 A358644 A358645 * A358647 A358648 A358649

Keyword

nonn,cons

Author

Stefano Spezia, Nov 24 2022

Status

approved