A241817 - OEIS

%I #14 Oct 14 2018 12:17:06

%S 6,10,14,22,26,34,46,62,74,82,86,106,134,142,166,194,202,214,226,254,

%T 274,314,334,362,382,386,422,446,466,482,502,526,566,622,634,662,694,

%U 746,842,862,866,886,914,922,974,1042,1094,1126,1154,1174,1226,1234,1262

%N Semiprimes sp such that sp-3 is prime.

%C Even numbers of the form 2p, p prime, that can be expressed as the sum of two primes in at least two ways as 2p = p + p = 3 + (2p-3). For example, 34 is in the sequence because 34 = 2*17 = 17 + 17 = 3 + 31. These are the only numbers that have Goldbach partitions with both a minimum and a maximum possible difference between their prime parts, i.e., |p-p| = 0 and |(2p-3)-3| = 2p-6 respectively. - _Wesley Ivan Hurt_, Apr 08 2018

%H K. D. Bajpai, <a href="/A241817/b241817.txt">Table of n, a(n) for n = 1..2500</a>

%F a(n) = 2 * A063908(n). - _Wesley Ivan Hurt_, Apr 08 2018

%e a(2) = 10 = 2*5, which is semiprime and 10-3 = 7 is a prime.

%e a(6) = 34 = 2*17, which is semiprime and 34-3 = 31 is a prime.

%p with(numtheory): A241817:= proc(); if bigomega(x)=2 and isprime(x-3) then  RETURN (x); fi; end: seq(A241817 (), x=1..3000);

%t 2 Select [Prime[Range[5!]], PrimeQ[2 # - 3] &] (* _Vincenzo Librandi_, Apr 10 2018 *)

%t Select[Range[1500],PrimeOmega[#]==2&&PrimeQ[#-3]&] (* _Harvey P. Dale_, Oct 14 2018 *)

%Y Cf. A001358, A063908, A092207, A123017, A198327.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Apr 29 2014