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 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified January 17 17:47 EST 2022. Contains 350402 sequences. (Running on oeis4.)