A219279
Primes of the form ChebyshevT[16,n].
Original entry on oeis.org
708158977, 21293229181234844660737, 21260958687099552174028801, 46453251497945783267589121, 64576903826545426454350012417, 26475257580698876650533675799180801, 352799899930156494230719582325262337, 423592588581159655917184553299009537
Offset: 1
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lst={}; Do[p=Abs[ChebyshevT[16, n]]; If[PrimeQ[p], AppendTo[lst, p]], {n, 10^3}]; lst
Select[ChebyshevT[16,Range[250]],PrimeQ] (* Harvey P. Dale, May 06 2013 *)
A219280
Smallest prime of the form ChebyshevT[2^n, x].
Original entry on oeis.org
2, 7, 97, 665857, 708158977, 150038171394905030432003281854339710977
Offset: 0
T(1, x) = x => a(0) = T(1,2) = 2 ;
T(2, x) = 2x^2 - 1 => a(1) = T(2, 2) = 7 ;
T(4, x) = 8x^4 - 8x^2 + 1 => a(2) = T(4,2) = 97.
- M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 795.
- C. W. Jones, J. C. P. Miller, J. F. C. Conn and R. C. Pankhurst, Tables of Chebyshev polynomials, Proc. Roy. Soc. Edinburgh. Sect. A. 62, (1946), 187-203.
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Table[k = 0; While[!PrimeQ[ChebyshevT[2^n,k]], k++]; ChebyshevT[2^n,k], {n, 0, 7}]
A219281
Smallest number k such that ChebyshevT[2^n, k] is prime.
Original entry on oeis.org
2, 2, 2, 3, 2, 8, 164, 29, 60, 213, 181, 652
Offset: 0
T(1, x) = x => T(1,2) = 2 is prime => a(0) = 2;
T(2, x) = 2x^2 - 1 => T(2, 2) = 7 is prime => a(1) = 2;
T(4, x) = 8x^4 - 8x^2 + 1 => T(4,2) = 97 is prime => a(2) = 2.
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for n from 0 to 11 do
P:= unapply(orthopoly[T](2^n,x),x):
for k from 1 do if isprime(P(k)) then A[n]:= k; break fi od
od:
seq(A[n],n=0..11); # Robert Israel, Aug 13 2018
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Table[k = 0; While[!PrimeQ[ChebyshevT[2^n,k]], k++]; k, {n, 0, 7}]
Showing 1-3 of 3 results.
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