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A369056
Numbers k of the form 4m+3 for which there is no representation as a sum (p*q + p*r + q*r) with three odd primes p <= q <= r.
9
3, 7, 11, 15, 19, 23, 31, 35, 43, 47, 59, 63, 67, 79, 83, 99, 107, 115, 127, 139, 143, 159, 163, 171, 175, 179, 207, 219, 223, 227, 235, 243, 259, 279, 283, 295, 303, 307, 319, 323, 339, 347, 367, 379, 387, 399, 403, 415, 427, 443, 463, 499, 515, 523, 531, 547, 559, 571, 579, 595, 603, 619, 639, 643, 655, 659, 675
OFFSET
1,1
COMMENTS
Numbers k in A004767 for which A369054(k) = 0.
Numbers k of the form 4m-1 such that they are not arithmetic derivative (A003415) of any term of A046316.
Question: Is it possible that this sequence might be finite (although very long)? See comments in A369055.
LINKS
MAPLE
N:= 1000: # for terms <= N
S:= {seq(i, i=3..N, 4)}:
P:= select(isprime, [seq(i, i=3..N/3, 2)]):
for i from 1 to nops(P) do
p:= P[i];
for j from i to nops(P) do
q:= P[j];
if 2*p*q + q^2 > N then break fi;
for k from j to nops(P) do
r:= P[k];
v:= p*q + p*r + q*r;
if v > N then break fi;
S:= S minus {v};
od od od:
sort(convert(S, list)); # Robert Israel, Apr 17 2024
PROG
(PARI) isA369056(n) = ((3==(n%4)) && !A369054(n)); \\ Needs also program from A369054.
CROSSREFS
Setwise difference A004767 \ A369251.
Subsequences: A369248 (terms that are multiples of 3), A369249 (primes in this sequence).
Cf. also A369250 (4m+3 primes missing from this sequence).
Sequence in context: A330213 A039957 A217332 * A079422 A310210 A292657
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 20 2024
STATUS
approved