A198196 Numbers k such that [V(4,1,k)/4] = floor(cosh(k log(sqrt(3)+2))/2) = A004526(A001075(k)) is a prime.

2, 3, 5, 7, 11, 13, 17, 19, 79, 151, 199, 233, 251, 317, 863, 971

Offset: 1

Author

M. F. Hasler, Oct 21 2011

Keywords

• nonn
• more

Comments

Further terms are 3049, 7451, 7487, 18869.

All terms must be primes. A117808 lists the corresponding primes floor(A001075(k)/2). Actually, the "floor" here and in the definition is only needed for the initial term 2, since no other even (thus composite) k can be in the sequence, and A001075(k) is even for odd k.

Links

• D. Broadhurst, Re: Cubic factors of n^n+(n+1)^(n+1), in "primenumbers" Yahoo group, Oct 21 2011.
• David Broadhurst, Cubic factors of n^n+(n+1)^(n+1), digest of 3 messages in primenumbers Yahoo group, Oct 21 - Oct 22, 2011.

Programs

PARI

q=2+quadgen(12); for(n=1,1e9, ispseudoprime(real(q^n)\2) & print1(n","))