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%I #8 Aug 13 2018 09:10:57
%S 2,2,2,3,2,8,164,29,60,213,181,652
%N Smallest number k such that ChebyshevT[2^n, k] is prime.
%C ChebyshevT[2^n,x] is the 2^n th Chebyshev polynomial of the first kind evaluated at x.
%e T(1, x) = x => T(1,2) = 2 is prime => a(0) = 2;
%e T(2, x) = 2x^2 - 1 => T(2, 2) = 7 is prime => a(1) = 2;
%e T(4, x) = 8x^4 - 8x^2 + 1 => T(4,2) = 97 is prime => a(2) = 2.
%p for n from 0 to 11 do
%p P:= unapply(orthopoly[T](2^n,x),x):
%p for k from 1 do if isprime(P(k)) then A[n]:= k; break fi od
%p od:
%p seq(A[n],n=0..11); # _Robert Israel_, Aug 13 2018
%t Table[k = 0; While[!PrimeQ[ChebyshevT[2^n,k]], k++]; k, {n, 0, 7}]
%Y Cf. A066436, A144131, A144132, A219276, A219277, A219278, A219279, A219280.
%K nonn,hard,more
%O 0,1
%A _Michel Lagneau_, Nov 17 2012
%E a(10) and a(11) from _Robert Israel_, Aug 13 2018
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