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%I A302258 #54 Jul 07 2021 08:36:39
%S A302258 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,
%T A302258 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,
%U A302258 9,5,4,0,5,2,7,6,7,9,3,7,3,9,7,5,5,7,2
%N A302258 Decimal expansion of the second radiation constant c_2 in meter-kelvin.
%C A302258 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.
%C A302258 It also appears in Planck's law when expressed in terms of the wavenumber. - _Charles R Greathouse IV_, Jun 25 2021
%C A302258 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
%C A302258 In natural (Planck) units this is 2*Pi = A019692. - _Charles R Greathouse IV_, Jul 07 2021
%H A302258 NIST, <a href="https://physics.nist.gov/cgi-bin/cuu/Value?c22ndrc">CODATA Value: second radiation constant</a>
%H A302258 Wikipedia, <a href="https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_base_units">2019 redefinition of the SI base units</a>
%H A302258 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sakuma%E2%80%93Hattori_equation">Sakuma-Hattori equation</a>
%H A302258 <a href="/index/Rec#order_9457">Index entries for linear recurrences with constant coefficients</a>, order 9457.
%F A302258 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
%e A302258 0.014387768775039338021466716015439115951990694231480991910326230635012954... m K.
%o A302258 (PARI) period(r,base=10)=
%o A302258 {
%o A302258   my(d=denominator(r),f=factor(base)[,1]);
%o A302258   for(i=1,#f,
%o A302258     d /= f[i]^valuation(d,f[i])
%o A302258   );
%o A302258   znorder(Mod(base,d));
%o A302258 }
%o A302258 rationalNumberOrder(r,base=10)=
%o A302258 {
%o A302258   my(f=factor(base)[,1],t,L,x='x,P);
%o A302258   for(i=1,#f,
%o A302258     t=valuation(r,f[i]);
%o A302258     if(t<0, r*=f[i]^-t)
%o A302258   );
%o A302258   r = frac(r);
%o A302258   L = period(r, base);
%o A302258   P = Polrev(digits(r*(base^L-1)));
%o A302258   poldegree(denominator(P/(1-x^L)));
%o A302258 }
%o A302258 rationalNumberOrder(272115870842319/18913000000000000) \\ _Kevin Ryde_ and _Charles R Greathouse IV_, Jul 05 2021
%Y A302258 Cf. A003678, A070063, A003676.
%K A302258 nonn,cons,easy
%O A302258 -1,2
%A A302258 _Felix Fröhlich_, Apr 12 2018
%E A302258 More terms from _Charles R Greathouse IV_, Jun 25 2021

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