A219281 Smallest number k such that ChebyshevT[2^n, k] is prime.

2, 2, 2, 3, 2, 8, 164, 29, 60, 213, 181, 652

Offset: 0

Author

Michel Lagneau, Nov 17 2012

Keywords

• nonn
• hard
• more

Comments

ChebyshevT[2^n,x] is the 2^n th Chebyshev polynomial of the first kind evaluated at x.

Examples

			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.
		

Crossrefs

Cf. A066436, A144131, A144132, A219276, A219277, A219278, A219279, A219280.

Programs

Maple

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

Mathematica

Table[k = 0; While[!PrimeQ[ChebyshevT[2^n,k]], k++]; k, {n, 0, 7}]

Extensions

a(10) and a(11) from Robert Israel, Aug 13 2018