|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
|