A350500 Even numbers that are both the sum of a twin prime pair and the sum of 1 and a semiprime.

36, 120, 144, 204, 216, 300, 396, 624, 696, 924, 1044, 1140, 1200, 1644, 1656, 1764, 2124, 2184, 2604, 2856, 3216, 3240, 3444, 3744, 3756, 3900, 4056, 4164, 4224, 4536, 4620, 4764, 5184, 5316, 5460, 5580, 5604, 6000, 6240, 6504, 6516, 6744, 7116, 7344, 7836, 7860, 8004

Offset: 1

Author

Wesley Ivan Hurt, Jan 01 2022

Keywords

• nonn

Examples

			36 is in the sequence since 36 = 17+19 = 1+35.
120 is in the sequence since 120 = 59+61 = 1+119.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Intersection of A054735 and A088707.

Cf. A349757.

Programs

Mathematica

Select[12 * Range[700], And @@ PrimeQ[#/2 + {-1, 1}] && PrimeOmega[# - 1] == 2 &] (* Amiram Eldar, Jan 02 2022 *)
Select[Total/@Select[Partition[Prime[Range[600]],2,1],#[[2]]-#[[1]]==2&],PrimeOmega[#-1]==2&] (* Harvey P. Dale, Feb 02 2025 *)

Python

from sympy import isprime, factorint
def ok(n): return n%2 == 0 and isprime(n//2-1) and isprime(n//2+1) and sum(factorint(n-1).values()) == 2
print([k for k in range(8005) if ok(k)]) # Michael S. Branicky, Jan 02 2022