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%I #100 Oct 06 2021 02:40:18
%S 3,4,25,98,119,123,136,267,299,318,344,423,429,443,444,522,552,571,
%T 577,588,589,639,677,739,771,817,933,993,1115,1212,1393,1503,1558,
%U 1580,1629,1756,1799,1852,1871,1884,1991,2027,2063,2197,2345,2380,2583,2585
%N Numbers k such that the area of an equilateral triangle of side k falls in between twin primes.
%C The number 3 is the only value where the area is between twin primes with 3 as one of the twins.
%e An equilateral triangle of side 3 has an area A = (sqrt(3)/4) * 3^2 = 3.89711, which is between 3 and 5, which are twin primes; so 3 is a term.
%e An equilateral triangle of side 17 has an area A = (sqrt(3)/4) * 17^2 = 125.14 which is between 125 and 127. These are not twin primes; so 17 is not a term.
%o (PARI) isok(k) = my(A = floor(k^2*sqrt(3)/4)); if (! (A%2), A--); isprime(A) && isprime(A+2); \\ _Michel Marcus_, Dec 28 2020
%Y Cf. A001359, A006512.
%K nonn
%O 1,1
%A _Philip Mizzi_, Dec 28 2020
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