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.
[ a: n in [0..350] | IsPrime(a) where a is n^2+n+3 ]; // Vincenzo Librandi, Dec 29 2010
npalQ[n_]:=Module[{c=n^2+n+3},c==IntegerReverse[c]]; Select[Range[ 0,31*10^5],npalQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 15 2016 *)
palQ[n_] := Block[{d = IntegerDigits[n]}, d == Reverse[d]]; f[n_] := n^2 + n + 3; Select[f@ Range[0, 10^5], palQ] (* Giovanni Resta, Aug 29 2018 *)
4 is in the list because 16+4+-3 = 23 and 17 are primes. 7 is in the list because 49+7+-3 = 53 and 59 are primes.
[k:k in [1..1750]| IsPrime(k^2+k+3) and IsPrime(k^2+k-3)]; // Marius A. Burtea, Feb 17 2020
q=3;lst3={};Do[p=n^2+n;If[PrimeQ[p-q]&&PrimeQ[p+q],AppendTo[lst3,n]],{n,0,7!}];lst3
Select[Range[2000],AllTrue[#^2+#+{3,-3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 01 2019 *)
seq(nextprime(n^2+n)-(n^2+n), n=0..100); # Robert Israel, Jul 05 2017
Table[k = 1; While[! PrimeQ[n^2 + n + k], k++]; k, {n, 0, 85}] (* Michael De Vlieger, Jul 04 2017 *)
for(n=0,85,k={my(k=1);while(!isprime(n^2+n+k),k++);k;};print1(k", "))
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