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A350500
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Even numbers that are both the sum of a twin prime pair and the sum of 1 and a semiprime.
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0
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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36 is in the sequence since 36 = 17+19 = 1+35.
120 is in the sequence since 120 = 59+61 = 1+119.
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MATHEMATICA
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Select[12 * Range[700], And @@ PrimeQ[#/2 + {-1, 1}] && PrimeOmega[# - 1] == 2 &] (* Amiram Eldar, Jan 02 2022 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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