A181669 Primes p of the form 6n-1 such that p-1 is a semiprime and p+2 is prime or prime squared.

5, 11, 23, 47, 59, 107, 167, 179, 227, 347, 359, 839, 1019, 1319, 1367, 1487, 1619, 2027, 2207, 2999, 3119, 3167, 3467, 4127, 4259, 4547, 4787, 4799, 5099, 5639, 5879, 6659, 6779, 6827, 7559, 8819, 10007, 10607, 11699, 12107, 12539, 14387, 14867, 15287, 15647

Offset

1,1

Comments

Except term 7, same as A181602.

Links

Table of n, a(n) for n=1..45.

Maple

isA181669 := proc(n::integer)
    if isprime(n) then
        if modp(n, 6) = 5 then
            if numtheory[bigomega](n-1) =2 then
                if isprime(n+2) or issqr(n+2) and isprime(sqrt(n+2)) then
                    true ;
                else
                    false;
                end if;
            else
                false;
            end if;
        else
            false;
        end if;
    else
        false;
    end if;
end proc:
for n from 2 to 100000 do
    if isA181669(n) then
        printf("%d, ", n) ;
    end if;
end do: # R. J. Mathar, Oct 17 2025

Mathematica

Select[6*Range[3000]-1, PrimeQ[#]&&PrimeOmega[#-1]==2&&AnyTrue[ {#+2, Sqrt[ #+2]}, PrimeQ]&] (* Harvey P. Dale, Jul 01 2022 *)

Crossrefs

Sequence in context: A337437 A107010 A175942 * A362082 A306662 A052940

Adjacent sequences: A181666 A181667 A181668 * A181670 A181671 A181672

Keyword

nonn

Author

Giovanni Teofilatto, Nov 18 2010

Status

approved