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(1) = -1 because there are an infinite number of nonprimes.
a(3) = 12 because 12 = Length[{1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17}] = Length[A124868(n)], where A124868(n) are the natural numbers that are not the sum of 3 distinct primes.
a(1) = 1 because 17 = 2+3+5+7 is the unique solution for the smallest such prime. a(2) = 2 because 23 = 2+3+5+13 = 2+3+7+11 are the only two solutions for the 2nd smallest such prime. a(3) = 3 because 29 = 2+3+5+19 = 2+3+7+17 = 2+3+11+13 are the only 3 solutions for the 3rd smallest such prime. a(4) = 3 because 31 = 2+3+7+19 = 2+5+7+17 = 2+5+11+13 are the only 3 solutions for the 4th smallest such prime. a(5) = 5 because 37 = 2+3+13+19 = 2+5+7+23 = 2+5+11+19 = 2+5+13+17 = 2+7+11+17 are the only 5 solutions for the 5th smallest such prime.
max=367;lim=PrimePi[max];p4=Sort[Total/@Subsets[Prime[Range[lim]],{4}]];p4p=Select[p4,PrimeQ[#]&&#<=max&]; s={};Do[c=Count[p4p,Prime[p]];If[c>0,AppendTo[s,c]],{p,lim}];s (* James C. McMahon, Jan 11 2025 *)
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