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%I #25 Apr 17 2024 15:33:25
%S 3,7,11,15,19,23,31,35,43,47,59,63,67,79,83,99,107,115,127,139,143,
%T 159,163,171,175,179,207,219,223,227,235,243,259,279,283,295,303,307,
%U 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
%N 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.
%C Numbers k in A004767 for which A369054(k) = 0.
%C Numbers k of the form 4m-1 such that they are not arithmetic derivative (A003415) of any term of A046316.
%C Question: Is it possible that this sequence might be finite (although very long)? See comments in A369055.
%H Antti Karttunen, <a href="/A369056/b369056.txt">Table of n, a(n) for n = 1..20000</a>
%p N:= 1000: # for terms <= N
%p S:= {seq(i,i=3..N,4)}:
%p P:= select(isprime, [seq(i,i=3..N/3,2)]):
%p for i from 1 to nops(P) do
%p p:= P[i];
%p for j from i to nops(P) do
%p q:= P[j];
%p if 2*p*q + q^2 > N then break fi;
%p for k from j to nops(P) do
%p r:= P[k];
%p v:= p*q + p*r + q*r;
%p if v > N then break fi;
%p S:= S minus {v};
%p od od od:
%p sort(convert(S,list)); # _Robert Israel_, Apr 17 2024
%o (PARI) isA369056(n) = ((3==(n%4)) && !A369054(n)); \\ Needs also program from A369054.
%Y Setwise difference A004767 \ A369251.
%Y Cf. A003415, A046316, A369054, A369055.
%Y Subsequences: A369248 (terms that are multiples of 3), A369249 (primes in this sequence).
%Y Cf. also A369250 (4m+3 primes missing from this sequence).
%K nonn
%O 1,1
%A _Antti Karttunen_, Jan 20 2024
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