OFFSET
0,1
COMMENTS
ChebyshevT[2^n,x] is the 2^n th Chebyshev polynomial of the first kind evaluated at x.
EXAMPLE
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.
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}]
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Michel Lagneau, Nov 17 2012
EXTENSIONS
a(10) and a(11) from Robert Israel, Aug 13 2018
STATUS
approved