

A219281


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


0



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

0,1


COMMENTS

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


LINKS



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:


MATHEMATICA

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


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



EXTENSIONS



STATUS

approved



