This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A335739 #100 Oct 06 2021 02:40:18 %S A335739 3,4,25,98,119,123,136,267,299,318,344,423,429,443,444,522,552,571, %T A335739 577,588,589,639,677,739,771,817,933,993,1115,1212,1393,1503,1558, %U A335739 1580,1629,1756,1799,1852,1871,1884,1991,2027,2063,2197,2345,2380,2583,2585 %N A335739 Numbers k such that the area of an equilateral triangle of side k falls in between twin primes. %C A335739 The number 3 is the only value where the area is between twin primes with 3 as one of the twins. %e A335739 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 A335739 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 A335739 (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 A335739 Cf. A001359, A006512. %K A335739 nonn %O A335739 1,1 %A A335739 _Philip Mizzi_, Dec 28 2020