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A354285
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Numbers k such that one of k, k+1, k+2 is prime and the other two are semiprimes, and one of R(n), R(n+1), R(n+2) is prime and the other two are semiprimes, where R = A004086.
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1
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4, 157, 177, 1381, 1437, 7417, 9661, 9901, 12757, 15297, 15681, 16921, 35961, 36901, 39777, 75741, 77277, 93097, 94441, 103317, 108201, 111261, 117541, 121377, 127597, 128461, 128901, 130197, 134677, 146841, 147417, 151377, 156601, 160077, 165441, 166861, 169177, 178537, 185901, 187881, 306541
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OFFSET
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1,1
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COMMENTS
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All terms after the first == 1 (mod 4).
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LINKS
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EXAMPLE
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a(3) = 177 is a term because 177 = 3*59 and 178 = 2*89 are semiprimes, 179 is prime, 771 = 3*257 and 871 = 13*67 are semiprimes and 971 is prime.
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MAPLE
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revdigs:= proc(n) local i, L;
L:= convert(n, base, 10);
add(10^(i-1)*L[-i], i=1..nops(L))
end proc:
f:= proc(n) uses numtheory;
if not isprime((n+1)/2) then return false fi;
if n mod 3 = 0 then if not(isprime(n/3) and isprime(n+2)) then return false fi
elif n mod 3 = 2 then return false
elif not(isprime(n) and isprime((n+2)/3)) then return false
fi;
sort(map(bigomega@revdigs, [n, n+1, n+2]))=[1, 2, 2]
end proc:
f(4):= true:
select(f, [4, seq(i, i=5..10^6, 4)]);
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MATHEMATICA
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Select[Range[300000], Sort[PrimeOmega[# + {0, 1, 2}]] == Sort[PrimeOmega[IntegerReverse[# + {0, 1, 2}]]] == {1, 2, 2} &] (* Amiram Eldar, May 29 2022 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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