OFFSET
1,1
COMMENTS
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
LINKS
K. D. Bajpai, Table of n, a(n) for n = 1..2500
FORMULA
a(n) = 2 * A063908(n). - Wesley Ivan Hurt, Apr 08 2018
EXAMPLE
a(2) = 10 = 2*5, which is semiprime and 10-3 = 7 is a prime.
a(6) = 34 = 2*17, which is semiprime and 34-3 = 31 is a prime.
MAPLE
MATHEMATICA
2 Select [Prime[Range[5!]], PrimeQ[2 # - 3] &] (* Vincenzo Librandi, Apr 10 2018 *)
Select[Range[1500], PrimeOmega[#]==2&&PrimeQ[#-3]&] (* Harvey P. Dale, Oct 14 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Apr 29 2014
STATUS
approved