OFFSET
1,1
COMMENTS
The associated p+4 are members of A063638.
Because all members of A023200 are == 1 (mod 3), the semiprimes p+2 are all == 0 (mod 3), so one of their two factors is 3.
The least-significant digit (LSD) of p > 13 in A023200 is always 3, 7 or 9, but those with LSD equal to 3 demand p+2 to have LSD 5 and therefore divisor 5 which contradicts the semiprime property above, so 13 is the only member of the sequence with LSD equal to 3.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
7 = prime(4), 11 = prime(5), (7+11)/2 = 3^2 = semiprime(3), so 7 is in the sequence.
13 = prime(6), 17 = prime(7), (13+17)/3 = 3 * 5 = semiprime(6), so 13 is in the sequence.
19 = prime(8), 23 = prime(9), (19+23)/3 = 3 * 7 = semiprime(7), so 19 is in the sequence.
MATHEMATICA
aQ[n_] := PrimeQ[n] && PrimeOmega[n + 2] == 2 && PrimeQ[n + 4]; Select[Range[12000], aQ] (* Amiram Eldar, Sep 08 2019 *)
Select[Prime[Range[1500]], PrimeQ[#+4]&&PrimeOmega[#+2]==2&] (* Harvey P. Dale, May 15 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 12 2010
STATUS
approved