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 A371029 #23 Mar 30 2024 12:27:12
%S A371029 1,5,6,7,13,29,39,40,45,81,120,122,127,142,143,205,214,241,293,334,
%T A371029 341,390,391,408,486,502,506,510,577,632,640,655,669,675,686,711,720,
%U A371029 792,793,794,802,851,859,891,901,909,972,974,992,1000,1041,1078,1082,1096,1099,1111,1206,1258,1280,1423
%N A371029 Numbers m such that if k = 27*m^3 + 3*m then k-1 and k+1 are primes.
%C A371029 Conjecture: this sequence is infinite.
%e A371029 1 is this sequence because 27*1^3 + 3*1 = 30 has 2 prime neighbors 29 and 31.
%t A371029 Select[Range[1500], And @@ PrimeQ[27*#^3 + 3*# + {-1, 1}] &] (* _Amiram Eldar_, Mar 26 2024 *)
%o A371029 (Magma) [m: m in [1..1500] | IsPrime(27*m^3+3*m-1) and IsPrime(27*m^3+3*m+1)];
%Y A371029 Numbers m such that (n*m)^n + n*m has 2 prime neighbors: A040040 (n=1); no sequence (n=2) in OEIS; this sequence (n=3); no sequence (n=4) in OEIS.
%Y A371029 Cf. A008585, A014574.
%K A371029 nonn
%O A371029 1,2
%A A371029 _Juri-Stepan Gerasimov_, Mar 25 2024