A283555 Even numbers that cannot be expressed as p+3, p+5, or p+7, with p prime.

98, 122, 124, 126, 128, 148, 150, 190, 192, 208, 210, 212, 220, 222, 224, 250, 252, 292, 294, 302, 304, 306, 308, 326, 328, 330, 332, 346, 348, 368, 398, 410, 418, 420, 430, 432, 458, 476, 478, 480, 488, 500, 518, 520, 522, 532, 534, 536, 538, 540, 542, 556

Offset: 1

Author

Keith Backman, Mar 10 2017

Keywords

• nonn

Comments

Any even number 2n which fails the Goldbach condition (i.e., is not expressible as the sum of two primes) cannot be a prime plus 3 (by definition), but it must also be the case that the two even numbers immediately smaller than 2n (i.e., 2n-2 and 2n-4) also cannot be a prime plus 3, because if they were, 2n would be a prime plus 5 or a prime plus 7 and would satisfy Goldbach. Thus any even number which fails the Goldbach condition must fall in this sequence. Note: none of the given members of the sequence fails Goldbach.

Crossrefs

Cf. A279040.

Programs

Mathematica

Select[2 Range[400], ! Or @@ PrimeQ[# - {3, 5, 7}] &] (* Giovanni Resta, Mar 10 2017 *)