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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
36 is in the sequence since 36 = 17+19 = 1+35.
120 is in the sequence since 120 = 59+61 = 1+119.
MATHEMATICA
Select[12 * Range[700], And @@ PrimeQ[#/2 + {-1, 1}] && PrimeOmega[# - 1] == 2 &] (* Amiram Eldar, Jan 02 2022 *)
PROG
(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
CROSSREFS
Intersection of A054735 and A088707.
Cf. A349757.
Sequence in context: A044287 A044668 A129367 * A287861 A242356 A165966
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jan 01 2022
STATUS
approved

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Last modified April 22 19:22 EDT 2024. Contains 371906 sequences. (Running on oeis4.)