A178041 Number of ways to represent the n-th prime (which has a nonzero number of such representations) as the sum of 4 distinct primes.

1, 2, 3, 3, 5, 6, 6, 6, 8, 10, 13, 14, 13, 18, 21, 17, 21, 30, 21, 32, 23, 37, 27, 45, 35, 34, 54, 43, 60, 61, 67, 44, 52, 55, 79, 58, 89, 57, 92, 100, 111, 69, 119, 76, 83, 122, 91, 89, 94, 102, 147, 146, 106, 159, 116, 176, 125, 190, 119, 195, 202, 136, 230, 148, 154, 222

Offset: 1

Author

Jonathan Vos Post, May 17 2010

Keywords

• easy
• nonn

Examples

			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.
		

Links

• Eric W. Weisstein, Goldbach Conjecture,

Crossrefs

Cf. A000040, A038609 (sum of 2 distinct primes), A124867 (sum of 3 distinct primes), A124868 (not the sum of 3 distinct primes), A124884 (not the sum of n distinct primes).

Programs

Mathematica

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 *)

Extensions

Extended by Zak Seidov