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A369250 Primes for which there is at least one representation as a sum (p*q + p*r + q*r) with three odd primes p <= q <= r.

%I A369250 #21 Jan 23 2024 16:41:06
%S A369250 71,103,131,151,167,191,199,211,239,251,263,271,311,331,359,383,419,
%T A369250 431,439,467,479,487,491,503,563,587,599,607,631,647,691,719,727,739,
%U A369250 743,751,811,823,839,859,863,887,911,919,971,983,991,1019,1031,1051,1063,1091,1103,1151,1163,1187,1223,1231,1279,1283,1291
%N A369250 Primes for which there is at least one representation as a sum (p*q + p*r + q*r) with three odd primes p <= q <= r.
%C A369250 All such primes are by necessity of the form 4m+3 (in A002145). See A369249 for those 4m+3 primes that do not have such a representation.
%C A369250 Also by necessity, in these cases the primes in the sum (p*q + p*r + q*r) must all be distinct, that is, we actually need p < q < r, otherwise the sum would not be a prime.
%H A369250 Antti Karttunen, <a href="/A369250/b369250.txt">Table of n, a(n) for n = 1..20000</a>
%H A369250 Antti Karttunen, <a href="https://oeis.org/plot2a?name1=A369250&amp;name2=A369249&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=matp&amp;drawlines=true">Primes with such a representation vs. 4m+3 primes without such a representation</a> (Plot2 comparison of the densities)
%e A369250 71 is present as 71 = (3*5) + (3*7) + (5*7) = A003415(105).
%o A369250 (PARI) isA369250(n) = (isprime(n) && (A369054(n)>0)); \\ Needs also program from A369054.
%Y A369250 Primes in A369251.
%Y A369250 Setwise difference A002145 \ A369249.
%Y A369250 Subsequence of A189441.
%Y A369250 Cf. A003415, A369054, A369056.
%K A369250 nonn
%O A369250 1,1
%A A369250 _Antti Karttunen_, Jan 22 2024