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%I #13 Jan 13 2023 18:39:21
%S 397,3581,6367,9949,14327,19501,25471,32237,39799,48157,67261,78007,
%T 115021,128951,143677,159199,192631,229247,248749,290141,312031,
%U 334717,433421,460087,544861,574711,735901,770527,842167,879181,1035197,1076191,1160567,1203949,1338871,1385437,1432799,1786621
%N Primes of the form 398*x^2-1.
%C There are 414 such primes for 1 <= x <= 1000, and 3280 for 1 <= x <= 10000.
%H V. Granville, <a href="https://mathoverflow.net/questions/375133/quadratic-progressions-with-very-high-prime-density">Quadratic progressions with very high prime density</a>, MathOverflow.
%F a(n) = 398*A338477(n)^2-1.
%e a(3) = 398*4^2-1 = 6367 is prime.
%p select(isprime, [seq(398*x^2-1,x=1..1000)]);
%t Select[398 Range[100]^2-1,PrimeQ] (* _Harvey P. Dale_, Jan 13 2023 *)
%Y Cf. A331947(11)=398, A338477.
%K nonn
%O 1,1
%A _Robert Israel_, Oct 29 2020