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.

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

Author

Antti Karttunen, Jan 20 2024

Keywords

• nonn

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

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Setwise difference A004767 \ A369251.

Cf. A003415, A046316, A369054, A369055.

Subsequences: A369248 (terms that are multiples of 3), A369249 (primes in this sequence).

Cf. also A369250 (4m+3 primes missing from this sequence).

Programs

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

PARI

isA369056(n) = ((3==(n%4)) && !A369054(n)); \\ Needs also program from A369054.