27679 is a semiprime n such that n-2 is also a semiprime and both have prime digit sums and prime sum of proper divisors.

Here 27679 = 89 * 311. Its sum of digits (31) is prime and its sum of proper divisors (401 = 311 + 89 + 1) is prime. The number 27677 = 13 * 2129 is also a semiprime with prime digit sum (29) and prime sum of proper divisors (2143).

The sequence can be generated as follows:

INPUT

L=[]

S=[n for n in [1..40000] if len(prime_factors(n))==2 and len(divisors(n))==4]

for s in S:

  P=prime_factors(s)

  D=s.digits()

  if is_prime(P[0]+P[1]+1) and is_prime(sum(D)):

    L.append(s)

M=[]

for i in range(2,len(L)):

  if L[i]-L[i-1]==2:

    M.append(L[i])

print(M)

print(len(M))

OUTPUT

[203, 205, 517, 1837, 2515, 2629, 2773, 4063, 4267, 4843, 5617, 6157, 7633, 9307, 10189, 10219, 11209, 11269, 11335, 11539, 11917, 12055, 12709, 13285, 14239, 15049, 16015, 16615, 17779, 19849, 21055, 23185, 23215, 23923, 26137, 27217, 27679, 29479, 29749, 31555, 31807, 35689, 38413]

43

27679 is a cyclic, Duffinian, happy and self number.

27679 can be rendered as a digit equation as follows:

2 ^ (7 - 6) + 7 = 9