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.

11, 23, 35, 47, 59, 83, 107, 143, 179, 227, 323, 347, 443, 515, 659, 683, 827, 947, 1259, 1523, 1763, 1787, 2075, 2267, 2675, 2963, 3023, 3203, 3275, 3347, 3467, 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

Offset: 1

Author

Antti Karttunen, Jan 23 2024

Keywords

• nonn

Comments

Equal to (12*i)-1, where i are the positions of 0's in A369462.

Terms of the form 3k+2 in A369056. These seem to be much more rare than terms of A369248.

Question: Is this a finite sequence, with the last term a(285) = 50688947 = (12*4224079)-1? See conjecture in A369055.

If it exists, a(286) > 201326603 (= (12*(2^24))+11).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..285 (please update, also comments, if more terms are found!)

Crossrefs

Intersection of A016789 and A369056 (and of A369464).

Subsequence of A017653.

Cf. A369054, A369055, A369462.

Cf. also A369248.

Programs

PARI

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])));
isA369463(n) = ((11==(n%12)) && !isA369251(n));