

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.


0



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
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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(k4)pi((k1)/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



