A347436 a(n) is the least odd number that has exactly n decompositions as the sum of three primes, or 0 if there is no such odd number.

1, 7, 9, 15, 17, 21, 31, 27, 35, 33, 39, 41, 45, 47, 55, 51, 53, 57, 0, 63, 67, 65, 71, 0, 79, 81, 0, 85, 77, 83, 99, 0, 0, 89, 97, 95, 103, 111, 101, 0, 0, 0, 115, 107, 0, 129, 121, 113, 0, 141, 119, 0, 0, 125, 133, 147, 0, 131, 159, 145, 153, 151, 137, 0, 0, 143, 0, 0, 149, 155, 0, 0, 0, 163, 189

Offset

0,2

Comments

Entries of 0 are conjectural. If nonzero they are greater than 10^5.

Assuming Goldbach's conjecture, if k is odd then A068307(k) >= pi(k-4)-pi((k-1)/2). Using Pierre Dusart's bounds on pi(x), this implies that, for example, A068307(k) >= 4292 for odd k >= 10^5. Thus (on the assumption of Goldbach's conjecture) the given entries of 0 are correct.

Links

Table of n, a(n) for n=0..74.

Example

a(3) = 15 because 15 has exactly 3 decompositions as the sum of 3 primes: 2+2+11 = 3+5+7 = 5+5+5, and it is the smallest odd number that does.

Maple

N:= 10^5:
P:= select(isprime, [2, seq(i, i=3..N, 2)]):
nP:=nops(P):
V:= Vector(N):
for i from 1 to nP do
  for j from i to nP while P[i]+P[j] <= N do
    for k from j to nP do
      n:= P[i]+P[j]+P[k];
      if n > N then break fi;
      V[n]:= V[n]+1;
od od od:
R:= Vector(300):
for i from 1 to N by 2 do
  if V[i] <= 300 and V[i] > 0 and R[V[i]] = 0 then R[V[i]]:= i fi
od:
convert(R, list);

Crossrefs

Cf. A068307, A139321.

Sequence in context: A073457 A067873 A217460 * A047522 A112072 A024902

Adjacent sequences: A347433 A347434 A347435 * A347437 A347438 A347439

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Sep 02 2021

Status

approved