A101411 Denominator when the numerator of the continued fraction rational approximation of sqrt(2) is prime. Also the denominators of A086395(n).
2, 5, 12, 29, 169, 408, 470832, 6625109, 44560482149, 345869461223138161, 13558774610046711780701, 87275373599917999482560755526644279276078854297832438763690789
Offset: 1
Crossrefs
Cf. A086395.
Programs
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Mathematica
Select[Convergents[Sqrt[2],200],PrimeQ[Numerator[#]]&]//Denominator (* Harvey P. Dale, Dec 27 2024 *)
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PARI
cfracnum(m,f) = { local(x,r,cfr,i,m1); default(realprecision,3000); numer2=0; denom2=0; cfr = vector(m+100); x=f; for(n=0,m, i=floor(x); x=1/(x-i); cfr[n+1] = i; ); for(m1=0,m, r=cfr[m1+1]; forstep(n=m1,1,-1, r = 1/r; r+=cfr[n]; ); numer=numerator(r); denom=denominator(r); if(ispseudoprime(numer),print1(denom",")); ); default(realprecision,28);