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A283555 Even numbers that cannot be expressed as p+3, p+5, or p+7, with p prime. 0

%I #8 Mar 12 2017 13:01:04

%S 98,122,124,126,128,148,150,190,192,208,210,212,220,222,224,250,252,

%T 292,294,302,304,306,308,326,328,330,332,346,348,368,398,410,418,420,

%U 430,432,458,476,478,480,488,500,518,520,522,532,534,536,538,540,542,556

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

%C 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.

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

%Y Cf. A279040.

%K nonn

%O 1,1

%A _Keith Backman_, Mar 10 2017

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Last modified March 28 04:58 EDT 2024. Contains 371235 sequences. (Running on oeis4.)