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 A111251 #76 Jan 17 2024 05:09:56 %S A111251 1,2,3,4,6,9,10,11,13,14,17,23,24,25,27,28,30,32,34,37,38,41,42,45,48, %T A111251 49,52,55,58,62,63,66,67,74,80,81,86,88,90,91,93,95,105,108,119,123, %U A111251 125,128,129,136,140,142,147,153,156,157,158,164,165,170,171,172,175 %N A111251 Numbers k such that 3*k^2 + 3*k + 1 is prime. %C A111251 That is, positive integers k such that (k+1)^3 - k^3 is prime. %C A111251 The Hardy-Littlewood constant 1.68109913... of this polynomial is approximately half that of the well-known Euler polynomial A221712, i.e., in comparison, only about half as many prime numbers are produced asymptotically as with k^2 + k + 41. - _Hugo Pfoertner_, Feb 10 2020 %C A111251 The primes that are obtained are called cuban primes and are in A002407. - _Bernard Schott_, Feb 13 2020 %H A111251 Daniel Starodubtsev, <a href="/A111251/b111251.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1965 from Pierre CAMI) %F A111251 a(n) = floor(sqrt(A002407(n)/3)). - _Rémi Guillaume_, Oct 16 2023 %F A111251 a(n) = A002504(n) - 1. - _Rémi Guillaume_, Oct 21 2023 %F A111251 a(n) = (A121259(n) - 1)/2. - _Rémi Guillaume_, Dec 29 2023 %e A111251 For k=52, 3*52^2 + 3*52 + 1 = 8269 is prime, so 52 is a term. %t A111251 Select[Range[200],PrimeQ[3#^2+3#+1]&] (* _Harvey P. Dale_, May 29 2017 *) %o A111251 (PARI) for(n=0,250,if(isprime(3*n^2+3*n+1),print1(n,","))) %o A111251 (Magma) [k: k in [1..180] | IsPrime(3*k^2 + 3*k + 1)]; // _Marius A. Burtea_, Feb 10 2020 %Y A111251 Cf. A221712, A002407 (resulting primes), A002504, A121259. %K A111251 nonn %O A111251 1,2 %A A111251 _Parthasarathy Nambi_, Oct 31 2005 %E A111251 Extended by Lambert Klasen (lambert.klasen(AT)gmx.net), Nov 02 2005