A219276 Numbers n such that T_4(n) is prime, where T_4(x) = 8x^4 - 8x^2 + 1 is the fourth Chebyshev polynomial (of the first kind).

2, 3, 5, 8, 10, 14, 17, 19, 31, 32, 34, 35, 39, 48, 50, 51, 53, 54, 59, 61, 73, 76, 78, 84, 88, 90, 97, 101, 102, 105, 107, 110, 121, 126, 128, 134, 135, 139, 143, 144, 146, 152, 153, 158, 167, 171, 172, 178, 180, 184, 186, 187, 189, 201, 202, 203, 205, 207

Offset: 1

Author

Michel Lagneau, Nov 17 2012

Keywords

• nonn

Comments

The corresponding primes are in A144131.

Sequence is infinite under Bunyakovsky's conjecture. - Charles R Greathouse IV, May 29 2013

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A144131.

Programs

Maple

filter:= n -> isprime(8*n^4 - 8*n^2+1):
select(filter, [$1..300]); # Robert Israel, Jan 22 2020

Mathematica

lst={}; Do[If[PrimeQ[ChebyshevT [4, n]], AppendTo[lst, n]], {n, 10^3}]; lst

PARI

is(n)=isprime(polchebyshev(4,1,n)) \\ Charles R Greathouse IV, May 29 2013