cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A161771 Decimal expansion of (70*exp(Pi*sqrt(163)))^2.

Original entry on oeis.org

3, 3, 7, 7, 3, 6, 8, 7, 5, 8, 7, 6, 9, 3, 5, 4, 7, 1, 4, 6, 6, 3, 1, 9, 6, 3, 2, 5, 0, 6, 0, 2, 4, 4, 6, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 2, 3, 1, 9, 3, 5, 6, 6, 2, 5, 2, 4, 9, 5, 7, 7, 1, 0, 4, 4, 1, 2, 4, 0, 6, 5, 9, 7, 4, 0, 9, 9, 7, 1, 0, 0, 6, 8, 5, 9, 8, 5, 1, 9, 3, 7, 0, 6, 5, 2, 2, 3, 2, 2, 8, 1, 6, 9
Offset: 39

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Author

Mark A. Thomas, Jun 18 2009

Keywords

Comments

Where exp^(Pi*sqrt163) is the Ramanujan constant and 70^2 is related to the norm vector 0 of the Leech lattice where 1^2 + 2^2 + 3^2 + ... + 22^2 + 23^2 + 24^2 = 70^2. A curiosity is: exp^2(Pi*sqrt163)*70^2 ~ hc/piGm^2 where all physics values are CODATA 2006 and m = neutron mass and exp^2(Pi*sqrt163)*70^2 = 3.377368...x 10^38 and hc/piGm^2 = 3.37700 x 10^38 (+- 0.00050) where 0.00050 = u_c which is the combined standard uncertainty.
This can also be expressed in a symmetric form in terms of the square of the neutron mass in units of Planck mass: where hc/2PiGm^2 = (Mp/m)^2 (Mp = Planck mass and m = neutron mass) and (exp^2(Pi*sqrt163)70^2)/2 ~ (Mp/m)^2. Note the divisor 2 in this case, which yields (exp^2(Pi*sqrt163)*70^2)/2 = 168868437938467735733159816253012231600.00000040115967. - Mark A. Thomas, Jul 02 2009

Examples

			337736875876935471466319632506024463200.00000080231935662524957710...
		

Crossrefs

Near relation to A160514 and A160515.

Programs

  • Magma
    SetDefaultRealField(RealField(100)); R:= RealField(); Exp(2*Pi(R)*Sqrt(163))*70^2; // G. C. Greubel, Oct 24 2018
  • Maple
    evalf((70*exp(Pi*sqrt(163)))^2,120); # Muniru A Asiru, Oct 25 2018
  • Mathematica
    First@ RealDigits[Exp[Pi Sqrt[163]]^2 70^2, 10, 105] (* Mark A. Thomas, Jun 18 2009, edited by Michael De Vlieger, Feb 19 2018 *)
  • PARI
    default(realprecision, 100); exp(2*Pi*sqrt(163))*70^2 \\ G. C. Greubel, Oct 24 2018
    

Formula

Equals exp(2*Pi*sqrt(163))*70^2.

A160514 A nonsense sequence.

Original entry on oeis.org

256, 9, 25, 49, 119663008743245277588690345984961
Offset: 1

Views

Author

Mark A. Thomas, May 16 2009

Keywords

Comments

Previous name was: The sequence is: 2^8, 3^2, 5^2, 7^2, 10939058860032031^2 where 10939058860032031 is prime and where its order is an integer 337736875876935471466319632507953926400 and is equal to ((640320)^3 + 744)^2 * 70^2 where (640320)^3 + 744 is an integer value which is nearly Ramanujan's constant and 1^2 + 2^2 + 3^2 + ... + 22^2 + 23^2 + 24^2 = 70^2 which is related to the norm vector 0 used in construction of the Leech lattice.
The prime number 10939058860032031 = 2^15, 3^2, 5^3, 23^3, 29^3 + 31 Ramanujan's constant: e^(Pi*sqrt(163))= 640320^3 + 743.99999999999925 = A060295.

Programs

  • Mathematica
    Power[#1, #2] & @@@ FactorInteger[(640320^3 + 744)^2*70^2] (* Michael De Vlieger, Dec 19 2015 *)

Formula

(640320^3 + 744)^2 * 70^2 = A160515.

Extensions

Partially edited by R. J. Mathar, May 30 2009

A212131 Decimal expansion of k such that e^(k*sqrt(163)) = round(e^(Pi*sqrt(163))).

Original entry on oeis.org

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

Views

Author

Omar E. Pol, Jun 25 2012

Keywords

Comments

Decimal expansion of log(262537412640768744)/sqrt(163).
First differs from A000796 at a(32).
Note that 262537412640768744 = 24*10939058860032031 = 2^3 * 3 * 10939058860032031, is the nearest integer to the value of Ramanujan's constant e^(Pi*sqrt(163)) = 262537412640768743.999999999999250... = A060295.

Examples

			3.14159265358979323846264338327972661934754988... (very close to Pi).
		

Crossrefs

Programs

  • Mathematica
    RealDigits[Log[Round[E^(Pi Sqrt[163])]]/Sqrt[163], 10, 105][[1]] (* Bruno Berselli, Jun 26 2012 *)

Formula

k = log(round(e^(Pi*sqrt(163))))/sqrt(163).

Extensions

More terms from Alois P. Heinz, Jun 25 2012
Showing 1-3 of 3 results.