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

1,2

Links

Table of n, a(n) for n=1..66.

Eric W. Weisstein, Goldbach Conjecture,

Example

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.

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 *)

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).

Sequence in context: A295918 A296834 A242642 * A181805 A369450 A212010

Adjacent sequences: A178038 A178039 A178040 * A178042 A178043 A178044

Keyword

easy,nonn,changed

Author

Jonathan Vos Post, May 17 2010

Extensions

Extended by Zak Seidov

Status

approved