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.

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

Offset: 1

Author

J. M. Bergot and Robert Israel, May 29 2022

Keywords

• nonn
• base

Comments

All terms after the first == 1 (mod 4).

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004086.

Programs

Maple

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)]);

Mathematica

Select[Range[300000], Sort[PrimeOmega[# + {0, 1, 2}]] == Sort[PrimeOmega[IntegerReverse[# + {0, 1, 2}]]] == {1, 2, 2} &] (* Amiram Eldar, May 29 2022 *)