A302258 Decimal expansion of the second radiation constant c_2 in meter-kelvin.

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

Offset

-1,2

Comments

Appears as a term in the Sakuma-Hattori equation for the electromagnetic signal from the thermal radiation emitted by an ideal black body of a given temperature.

It also appears in Planck's law when expressed in terms of the wavenumber. - Charles R Greathouse IV, Jun 25 2021

The exact value, following the 2019 redefinition of SI units, is 272115870842319/18913000000000000. Hence, periodic with period 18912. - Charles R Greathouse IV, Jun 25 2021

In natural (Planck) units this is 2*Pi = A019692. - Charles R Greathouse IV, Jul 07 2021

Links

Table of n, a(n) for n=-1..85.

NIST, CODATA Value: second radiation constant

Wikipedia, 2019 redefinition of the SI base units

Wikipedia, Sakuma-Hattori equation

Index entries for linear recurrences with constant coefficients, order 9457.

Formula

c_2 = h*c/k where k is Planck's constant, c is the speed of light in a vacuum, and k is the Boltzmann constant. - Charles R Greathouse IV, Jun 25 2021

Example

0.014387768775039338021466716015439115951990694231480991910326230635012954... m K.

Prog

(PARI) period(r, base=10)=
{
  my(d=denominator(r), f=factor(base)[, 1]);
  for(i=1, #f,
    d /= f[i]^valuation(d, f[i])
  );
  znorder(Mod(base, d));
}
rationalNumberOrder(r, base=10)=
{
  my(f=factor(base)[, 1], t, L, x='x, P);
  for(i=1, #f,
    t=valuation(r, f[i]);
    if(t<0, r*=f[i]^-t)
  );
  r = frac(r);
  L = period(r, base);
  P = Polrev(digits(r*(base^L-1)));
  poldegree(denominator(P/(1-x^L)));
}
rationalNumberOrder(272115870842319/18913000000000000) \\ Kevin Ryde and Charles R Greathouse IV, Jul 05 2021

Crossrefs

Cf. A003678, A070063, A003676.

Sequence in context: A360689 A110662 A265289 * A132021 A089368 A357130

Adjacent sequences: A302255 A302256 A302257 * A302259 A302260 A302261

Keyword

nonn,cons,easy

Author

Felix Fröhlich, Apr 12 2018

Extensions

More terms from Charles R Greathouse IV, Jun 25 2021

Status

approved