A238572 Primes that can be expressed in more than one way in the form p * q + r such that p, q, and r are all prime, p > q, and p >= r.

17, 29, 37, 41, 53, 59, 67, 71, 79, 89, 97, 101, 103, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 173, 179, 181, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353

Offset

1,1

Comments

The sequence seems to contain all the primes except for 2, 3, 5, 7, 11, 13, 19, 23, 31, 43, 47, 61, 73, 83, 107, 167, and 191 (tested up to 10^7). - Giovanni Resta, Mar 04 2014

It follows that (up to 10^7), 2 the only non-odd prime, along with two odd primes, by p * q +- r is sufficient to generate all odd primes, since 3, 5, 7, 11, 83, 167, not generated by p * q + r, are generated by p * q - r. - Torlach Rush, Mar 05 2014

Links

Giovanni Resta, Table of n, a(n) for n = 1..1000

Example

a(1) = 17 = 5 * 3 + 2 = 7 * 2 + 3.

Mathematica

decQ[n_] := Block[{c = If[{1, 1} == Last /@ FactorInteger[n-2], 1, 0], r=3},
While[c < 2 && 3*r < n, If[PrimeQ[(n - r)/2], ++c]; r = NextPrime@r]; c > 1]; Select[Prime@ Range@ 90, decQ] (* Giovanni Resta, Mar 04 2014 *)

Crossrefs

Cf. A000040

Sequence in context: A350101 A360972 A319265 * A266965 A081985 A087937

Adjacent sequences: A238569 A238570 A238571 * A238573 A238574 A238575

Keyword

nonn

Author

Torlach Rush, Feb 28 2014

Status

approved