A392481 - OEIS

%I #10 Jan 15 2026 17:50:15

%S 10,16,85,169,211,229,289,349,361,445,451,484,544,700,826,835,844,955,

%T 1066,1111,1156,1231,1351,1420,1480,1501,1576,1855,1945,2044,2050,

%U 2086,2116,2161,2200,2335,2350,2494,2620,2659,2815,3214,3250,3271,3334,3400,3406,3454,3520,3571,3664,3715,3769,3871

%N Numbers k such that both (3*k-3)^2 + k^2 and (3*k)^2 + (k+1)^2 are prime.

%C All terms == 1 (mod 3).

%H Robert Israel, <a href="/A392481/b392481.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 85 is a term because (3*85-3)^2 + 85^2 = 70729 and (3*85)^2 + 86^2 = 72421 are both primes.

%p filter:= t -> isprime((3*t-3)^2 + t^2) and isprime((3*t)^2 + (t+1)^2):

%p select(filter, [$1..10000]);

%t Select[Range[1, 5000, 3], PrimeQ[2*#*(5*#-9) + 9] && PrimeQ[2*#*(5*#+1) + 1] &] (* _Paolo Xausa_, Jan 15 2026 *)

%K nonn

%O 1,1

%A _Will Gosnell_ and _Robert Israel_, Jan 13 2026