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(5)=5 as A000040(5)=11 and there are no more representations not containing 11 than 11 = (3+7+23)/3 = (3+13+17)/3 = (5+5+23)/3 = (7+7+19)/3 = (7+13+13)/3.
a071704 n = z (us ++ vs) 0 (3 * q) where z _ 3 m = fromEnum (m == 0) z ps'@(p:ps) i m = if m < p then 0 else z ps' (i+1) (m - p) + z ps i m (us, _:vs) = span (< q) a065091_list; q = a000040 n -- Reinhard Zumkeller, May 24 2015
N:= 300: # to get the first A000720(N) terms P:= select(isprime, [seq(i,i=3..3*N,2)]): nP:= nops(P): V:= Vector(N): for i from 1 to nP do for j from i to nP do for k from j to nP while P[i]+P[j]+P[k] <= 3*N do r:= (P[i]+P[j]+P[k])/3; if r::integer and isprime(r) and r <> P[j] and r <= N then V[r]:= V[r]+1 fi od od od: seq(V[ithprime(i)],i=1..numtheory:-pi(N)); # Robert Israel, Aug 09 2018
M = 300; (* to get the first A000720(M) *) P = Select[Range[3, 3*M, 2], PrimeQ]; nP = Length[P]; V = Table[0, {M}]; For[i = 1, i <= nP, i++, For[j = i, j <= nP, j++, For[k = j, k <= nP && P[[i]] + P[[j]] + P[[k]] <= 3*M , k++, r = (P[[i]] + P[[j]] + P[[k]])/3; If[IntegerQ[r] && PrimeQ[r] && r != P[[j]] && r <= M, V[[r]] = V[[r]]+1] ]]]; Table[V[[Prime[i]]], {i, 1, PrimePi[M]}] (* Jean-François Alcover, Mar 09 2019, after Robert Israel *)
a(n, p=prime(n))=my(s=0); forprime(q=p+2, 3*p-4, my(t=3*p-q); forprime(r=max(t-q, 3), (3*p-q)\2, if(t!=p+r && isprime(t-r), s++))); s \\ Charles R Greathouse IV, Jun 04 2015
3 * 2 - 4 = 2, 3 * 3 - 4 = 5, 3 * 5 - 4 = 11, 3 * 7 - 4 = 17, 3 * 11 - 4 = 29 are all prime, so 2, 3, 5, 7, 11 are all in the sequence. 3 * 13 - 4 = 35 = 5 * 7, so 13 is not in the sequence.
[p: p in PrimesUpTo(1000) | IsPrime(3*p-4)]; // Vincenzo Librandi, May 25 2015
Select[Prime[Range[200]], PrimeQ[3# - 4] &]
forprime(p=1,10^3,if(isprime(3*p-4),print1(p,", "))) \\ Derek Orr, May 27 2015
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