OFFSET
1,1
COMMENTS
It is conjectured that all terms are prime. See Leung et al. p. 12.
All terms up to 10^9 are prime.
Since the Diophantine equation 12*c^2 + 4*c + 3 = x^2 has no solution, all terms p^e have either e=1 or e>=3 and odd. Up to 10^24, all terms are prime. - Giovanni Resta, Jul 08 2019
It appears that these are the primes of A271723. - Bill McEachen, Aug 14 2021
LINKS
Ka Hin Leung, Koji Momihara and Qing Xiang, A new family of Hadamard matrices of order 4(2q^2+1), arXiv:1907.02623 [math.CO], 2019. See p. 3.
PROG
(PARI) isok(n) = isprimepower(n) && issquare(3*n-8) && (d=sqrtint(3*n-8)) && ((frac((d-1)/6) == 0) || (frac((d+1)/6) == 0));
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Jul 08 2019
STATUS
approved