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A354285 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.

%I A354285 #49 May 30 2022 19:35:40
%S A354285 4,157,177,1381,1437,7417,9661,9901,12757,15297,15681,16921,35961,
%T A354285 36901,39777,75741,77277,93097,94441,103317,108201,111261,117541,
%U A354285 121377,127597,128461,128901,130197,134677,146841,147417,151377,156601,160077,165441,166861,169177,178537,185901,187881,306541
%N A354285 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.
%C A354285 All terms after the first == 1 (mod 4).
%H A354285 Robert Israel, <a href="/A354285/b354285.txt">Table of n, a(n) for n = 1..10000</a>
%e A354285 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.
%p A354285 revdigs:= proc(n) local i,L;
%p A354285   L:= convert(n,base,10);
%p A354285   add(10^(i-1)*L[-i],i=1..nops(L))
%p A354285 end proc:
%p A354285 f:= proc(n) uses numtheory;
%p A354285       if not isprime((n+1)/2) then return false fi;
%p A354285       if n mod 3 = 0 then if not(isprime(n/3) and isprime(n+2)) then return false fi
%p A354285       elif n mod 3 = 2 then return false
%p A354285       elif not(isprime(n) and isprime((n+2)/3)) then return false
%p A354285       fi;
%p A354285       sort(map(bigomega@revdigs,[n,n+1,n+2]))=[1,2,2]
%p A354285 end proc:
%p A354285 f(4):= true:
%p A354285 select(f, [4, seq(i,i=5..10^6,4)]);
%t A354285 Select[Range[300000], Sort[PrimeOmega[# + {0, 1, 2}]] == Sort[PrimeOmega[IntegerReverse[# + {0, 1, 2}]]] == {1, 2, 2} &] (* _Amiram Eldar_, May 29 2022 *)
%Y A354285 Cf. A004086.
%K A354285 nonn,base
%O A354285 1,1
%A A354285 _J. M. Bergot_ and _Robert Israel_, May 29 2022