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

1,1

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!)

Prog

(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));

Crossrefs

Intersection of A016789 and A369056 (and of A369464).

Subsequence of A017653.

Cf. A369054, A369055, A369462.

Cf. also A369248.

Sequence in context: A041549 A136771 A017653 * A180316 A139793 A101859

Adjacent sequences: A369460 A369461 A369462 * A369464 A369465 A369466

Keyword

nonn

Author

Antti Karttunen, Jan 23 2024

Status

approved