A272001 -id:A272001 - cp's OEIS frontend

A020793 Decimal expansion of 1/6.

1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset: 0

N. J. A. Sloane

Except for the first term identical to A010722, A040006 and A021019. Except for the first terms the same as A021028, A021100, A021388, A071279, A101272, A168608, A177057,... - M. F. Hasler, Oct 24 2011

Decimal expansion of gamma(1) = 5/3 (with offset 1), where gamma(n) = Cp(n)/Cv(n) = is the n-th Poisson's constant. For the definition of Cp and Cv see A272002. - Natan Arie Consigli, Jul 10 2016

Calvin C. Clawson, Mathematical Mysteries, The Beauty and Magic of Numbers, Springer, 2013, see p. 224.

Wikipedia, Poisson's constant.
Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A010722, A021019, A021028, A021100, A021388, A040006, A070064, A071279, A081822, A101272, A168608, A177057, A272001, A272002.

RealDigits[1/6,10,120][[1]] (* or *) PadRight[{1},120,{6}] (* Harvey P. Dale, Dec 30 2018 *)

a(n)=6-5*!n  \\ M. F. Hasler, Oct 24 2011

a(n) = 6^n mod 10. - Zerinvary Lajos, Nov 26 2009
Equals Sum_{k>=1} 1/7^k. - Bruno Berselli, Jan 03 2014
10 * 1/6 = 5/3 = (5/2 R)/(3/2 R) = Cp(1)/Cv(1) = A272002/A272001, with R = A081822 (or A070064). - Natan Arie Consigli, Jul 10 2016
G.f.: (1 + 5*x)/(1 - x). - Ilya Gutkovskiy, Jul 10 2016
Equals Sum_{k>=1} 1/(k*Pi)^2. - Maciej Kaniewski, Sep 14 2017
Equals Sum_{k>=1} (zeta(2*k)-1)/4^k. - Amiram Eldar, Jun 08 2021
K_{n>=2} 2*n/(2*n - 3) = 5/3. (see Clawson at p. 224). - Stefano Spezia, Jul 01 2024
E.g.f.: 6*exp(x) - 5. - Elmo R. Oliveira, Aug 05 2024

A272002 Decimal expansion of Cp(1), the molar specific heat of an atomic ideal gas at constant pressure.

Original entry on oeis.org

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

Offset: 2

Natan Arie Consigli, Jul 06 2016

Also the decimal expansion of the molar specific heat of an ideal gas consisting of molecules with 5 degrees of freedom at constant volume.
The molar specific heat of an ideal gas consisting of molecules with n degrees of freedom at constant pressure and volume can be calculated respectively with the following formulae:
- Cv(n) = n/2 R;
- Cp(n) = (1 + n/2) R;
Where R = Cp(n) - Cv(n) = A070064 is the molar gas constant.
Molecules of a monatomic gas have 3 degrees of freedom. Diatomic and polyatomic molecules can have additional degrees of freedom.

			Cp(1) = 20.7861565453831 J mol^-1 K^-1.

Wikipedia, Molar heat capacity.

Cf. A070064, A272001, A272003, A272004, A272005.

Cp(1) = (1 + 3/2) * R = 5/2 * A070064.

Cp(1) = Cv(1) + R = A272001 + A070064.

Edited by Andrey Zabolotskiy, Mar 28 2025

A272003 Decimal expansion of the molar specific heat of an ideal gas consisting of molecules with 5 degrees of freedom at constant pressure, in J mol^-1 K^-1.

Original entry on oeis.org

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

Offset: 2

Natan Arie Consigli, Jul 06 2016

Also the decimal expansion of the molar specific heat of an ideal gas consisting of molecules with 7 degrees of freedom at constant volume.

			29.10061916353634 J mol^-1 K^-1.

Cf. A070064, A272001, A272002.

Equals 7/2 * R = 7/2 * A070064.

Equals A272002 + A070064.

Edited by Andrey Zabolotskiy, Apr 02 2025

A272005 Decimal expansion of the molar specific heat of an ideal gas consisting of molecules with 9 degrees of freedom at constant pressure, in J mol^-1 K^-1.

Original entry on oeis.org

4, 5, 7, 2, 9, 5, 4, 4, 3, 9, 9, 8, 4, 2, 8, 2

Offset: 2

Natan Arie Consigli, Jul 09 2016

Also the decimal expansion of the molar specific heat of an ideal gas consisting of molecules with 11 degrees of freedom at constant volume.

			45.72954439984282 J mol^-1 K^-1.

Kshitij Education, Molar specific heat [Wayback Machine link].
Wikipedia, Molar heat capacity.

Cf. A070064, A272001, A272002, A272003, A272004.

Equals 11/2 * R = 11/2 * A070064.

Equals A272004 + A070064.

Edited by Andrey Zabolotskiy, Apr 02 2025

A272004 Decimal expansion of the molar specific heat of an ideal gas consisting of molecules with 7 degrees of freedom at constant pressure, in J mol^-1 K^-1.

Original entry on oeis.org

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

Offset: 2

Natan Arie Consigli, Jul 09 2016

Also the decimal expansion of the molar specific heat of an ideal gas consisting of molecules with 9 degrees of freedom at constant volume.

			37.41508178168958 J mol^-1 K^-1.

Wikipedia, Molar heat capacity.

Cf. A070064, A272001, A272002, A272003, A272005.

Equals 9/2 * R = 9/2 * A070064.

Equals A272003 + A070064.

Edited by Andrey Zabolotskiy, Apr 02 2025

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A020793 Decimal expansion of 1/6.

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A272002 Decimal expansion of Cp(1), the molar specific heat of an atomic ideal gas at constant pressure.

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A272003 Decimal expansion of the molar specific heat of an ideal gas consisting of molecules with 5 degrees of freedom at constant pressure, in J mol^-1 K^-1.

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A272005 Decimal expansion of the molar specific heat of an ideal gas consisting of molecules with 9 degrees of freedom at constant pressure, in J mol^-1 K^-1.

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A272004 Decimal expansion of the molar specific heat of an ideal gas consisting of molecules with 7 degrees of freedom at constant pressure, in J mol^-1 K^-1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

Extensions