cp's OEIS Frontend

A369463 Numbers of the form 12*m-1 for which there is no representation as a sum (p*q + p*r + q*r) with three odd primes p <= q <= r.

%I A369463 #20 Jan 25 2024 23:19:11
%S A369463 11,23,35,47,59,83,107,143,179,227,323,347,443,515,659,683,827,947,
%T A369463 1259,1523,1763,1787,2075,2267,2675,2963,3023,3203,3275,3347,3467,
%U A369463 3635,4523,4643,4859,5003,5147,5747,5819,6395,6803,6827,7235,8003,8123,8171,8747,8963,9323,9659,9827,10367,10427,12347,12923,13187
%N A369463 Numbers of the form 12*m-1 for which there is no representation as a sum (p*q + p*r + q*r) with three odd primes p <= q <= r.
%C A369463 Equal to (12*i)-1, where i are the positions of 0's in A369462.
%C A369463 Terms of the form 3k+2 in A369056. These seem to be much more rare than terms of A369248.
%C A369463 Question: Is this a finite sequence, with the last term a(285) = 50688947 = (12*4224079)-1? See conjecture in A369055.
%C A369463 If it exists, a(286) > 201326603 (= (12*(2^24))+11).
%H A369463 Antti Karttunen, <a href="/A369463/b369463.txt">Table of n, a(n) for n = 1..285</a> (please update, also comments, if more terms are found!)
%o A369463 (PARI)
%o A369463 isA369251(n) =  if(3!=(n%4),0, my(v = [3,3], ip = #v, r); while(1, r = (n-(v[1]*v[2])) / (v[1]+v[2]); if(r < v[2], ip--, ip = #v; if(1==denominator(r) && isprime(r), return(1))); if(!ip, return(0)); v[ip] = nextprime(1+v[ip]); for(i=1+ip,#v,v[i]=v[i-1])));
%o A369463 isA369463(n) = ((11==(n%12)) && !isA369251(n));
%Y A369463 Intersection of A016789 and A369056 (and of A369464).
%Y A369463 Subsequence of A017653.
%Y A369463 Cf. A369054, A369055, A369462.
%Y A369463 Cf. also A369248.
%K A369463 nonn
%O A369463 1,1
%A A369463 _Antti Karttunen_, Jan 23 2024