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

%I A350500 #17 Feb 02 2025 14:42:15
%S A350500 36,120,144,204,216,300,396,624,696,924,1044,1140,1200,1644,1656,1764,
%T A350500 2124,2184,2604,2856,3216,3240,3444,3744,3756,3900,4056,4164,4224,
%U A350500 4536,4620,4764,5184,5316,5460,5580,5604,6000,6240,6504,6516,6744,7116,7344,7836,7860,8004
%N A350500 Even numbers that are both the sum of a twin prime pair and the sum of 1 and a semiprime.
%H A350500 Harvey P. Dale, <a href="/A350500/b350500.txt">Table of n, a(n) for n = 1..1000</a>
%e A350500 36 is in the sequence since 36 = 17+19 = 1+35.
%e A350500 120 is in the sequence since 120 = 59+61 = 1+119.
%t A350500 Select[12 * Range[700], And @@ PrimeQ[#/2 + {-1, 1}] && PrimeOmega[# - 1] == 2 &] (* _Amiram Eldar_, Jan 02 2022 *)
%t A350500 Select[Total/@Select[Partition[Prime[Range[600]],2,1],#[[2]]-#[[1]]==2&],PrimeOmega[#-1]==2&] (* _Harvey P. Dale_, Feb 02 2025 *)
%o A350500 (Python)
%o A350500 from sympy import isprime, factorint
%o A350500 def ok(n): return n%2 == 0 and isprime(n//2-1) and isprime(n//2+1) and sum(factorint(n-1).values()) == 2
%o A350500 print([k for k in range(8005) if ok(k)]) # _Michael S. Branicky_, Jan 02 2022
%Y A350500 Intersection of A054735 and A088707.
%Y A350500 Cf. A349757.
%K A350500 nonn
%O A350500 1,1
%A A350500 _Wesley Ivan Hurt_, Jan 01 2022