A284983 -id:A284983 - cp's OEIS frontend

A118858 Decimal expansion of log(2)/Pi^2.

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

Offset: 0

Eric W. Weisstein, May 02 2006

			0.07023049277268287640...

Derrick Norman Lehmer, Asymptotic Evaluation of Certain Totient Sums, American Journal of Mathematics, Vol. 22, No. 4 (1900), pp. 293-335.
Eric Weisstein's World of Mathematics, Primitive Pythagorean Triple.

Cf. A249750, A328499, A002162, A002388, A284983.

RealDigits[Log[2]/Pi^2, 10, 100][[1]] (* Amiram Eldar, Jun 25 2021 *)

log(2)/Pi^2 \\ Michel Marcus, Jun 25 2021

Equals lim_{n->oo} A328499(n)/n. - Amiram Eldar, Jun 25 2021

Equals Integral_{z>=0} z*sech(Pi*z)^2. - Peter Luschny, Aug 03 2021

A185361 Decimal expansion of 2^(1/Pi).

Original entry on oeis.org

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

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 26 2012

			1.2468689889006383054973706361255770054725456343911...

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A000796, A049541, A284983.

Mathematica
```
RealDigits[N[2^(1/Pi),200]][[1]]
```
PARI
```
2^(1/Pi) \\ G. C. Greubel, Jun 28 2017
```

Equals exp(A284983). - Amiram Eldar, Nov 24 2020

A359532 Decimal expansion of 2*log(2)/Pi.

Original entry on oeis.org

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

Offset: 0

Stefano Spezia, Jan 04 2023

2*log(2)*n/Pi is also the dominant term in the asymptotic expansion of Sum_{k=1..n-1} (-1)^(k+1)*csc(Pi*k/n) at n tending to infinity. - Iaroslav V. Blagouchine, Apr 10 2025

			0.441271200305303186792912864235995381965...

Iaroslav V. Blagouchine, On a Generalization of Watson's Trigonometric Sum (On Dowker's Sum of Order One Half), INTEGERS, Electronic Journal of Combinatorial Number Theory, vol. 25, Article #A30, pp. 1-33, 2025. See p. 18.
John M. Campbell, Applications of a class of transformations of complex sequences, arXiv:2212.13305 [math.NT], 2022. See pp. 2, 8.

Cf. A000796, A001008, A002162, A002805, A002897, A016627, A016813, A060294.

Cf. A359533.

Mathematica
```
First[RealDigits[N[2Log[2]/Pi,98]]]
```

Equals A016627/A000796.
Equals A002162*A060294.
Equals 2*A284983.
Equals Sum_{i>=0} (-1/64)^i*binomial(2*i, i)^3*(4*i + 1)*H_{2*i}, where H_m is the m-th harmonic number (negated).

cp's OEIS Frontend

A118858 Decimal expansion of log(2)/Pi^2.

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A185361 Decimal expansion of 2^(1/Pi).

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A359532 Decimal expansion of 2*log(2)/Pi.

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