A273457 Even numbers 2n that do not have a Goldbach partition 2n = p + q (p < q; p, q prime) satisfying sqrt(n) < p <= sqrt(2n).

2, 4, 6, 8, 12, 18, 20, 22, 24, 26, 30, 32, 38, 40, 44, 52, 56, 58, 62, 64, 70, 72, 76, 82, 84, 88, 92, 94, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 126, 128, 130, 132, 134, 136, 140, 144, 146, 152, 154, 156, 158, 164, 166, 172, 182, 188, 196, 198, 200, 214

Offset

1,1

Comments

This is an extension of A244408.

There are 74 elements of A279040 that are also in this sequence. These common elements are in A244408.

It is conjectured that a(12831) = 15702604 is the last term. There are no more terms below 4*10^10.

Links

Corinna Regina Böger, Table of n, a(n) for n = 1..12831

Example

32 is in the sequence because 32 has two Goldbach partitions: 32 = 3 + 29 with 3 < sqrt(16) and 32 = 13 + 19 with 13 > sqrt(32).

Mathematica

noGoldbatSqrQ[n_] := Block[{p = NextPrime[Sqrt[n/2]]}, While[2p < n && !PrimeQ[n - p], p = NextPrime@ p]; p > Sqrt[n]]; noGoldbatSqrQ[4] = True; Select[2Range[107], noGoldbatSqrQ] (* Robert G. Wilson v, Dec 15 2016 *)

Prog

(PARI) noSpecialGoldbach(n) = forprime(p=sqrtint(n/2-1) + 1, sqrtint(n), if(p<(n-p) && isprime(n-p), return(0))); 1
is(n) = n%2 == 0 && noSpecialGoldbach(n)

Crossrefs

Cf. A002373, A020481, A025018, A025019, A244408, A279040.

Sequence in context: A081954 A096903 A352107 * A222603 A177710 A032458

Adjacent sequences: A273454 A273455 A273456 * A273458 A273459 A273460

Keyword

nonn

Author

Corinna Regina Böger, Dec 11 2016

Status

approved