A357934 Products of two distinct lesser twin primes A001359.

15, 33, 51, 55, 85, 87, 123, 145, 177, 187, 205, 213, 295, 303, 319, 321, 355, 411, 447, 451, 493, 505, 535, 537, 573, 591, 649, 681, 685, 697, 717, 745, 781, 807, 843, 895, 933, 955, 985, 1003, 1041, 1111, 1135, 1177, 1189, 1195, 1207, 1257, 1293, 1345, 1383, 1405, 1507, 1555, 1563

Offset: 1

Author

Artur Jasinski, Oct 21 2022

Keywords

• nonn

Links

• R. J. Mathar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001359. Subsequence of A006881.

Programs

Maple

omega := proc(n)
    nops(numtheory[factorset](n)) ;
end proc:
isA357934 := proc(n)
    local pe,p,q;
    if numtheory[bigomega](n)= 2 and omega(n) =2 then
        pe := ifactors(n)[2] ;
        p := op(1,op(1,pe)) ;
        q := op(1,op(2,pe)) ;
        if isprime(p+2) and isprime(q+2) then
            true;
        else
            false;
        end if;
    else
        false;
    end if;
end proc:
for n from 10 to 2000 do
    if isA357934(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Feb 13 2025

Mathematica

d = {};less = Select[Range[1607], PrimeQ[#] && PrimeQ[# + 2] &];Do[Do[AppendTo[d, less[[m]] less[[n]]], {m, n + 1, Length[less]}], {n,
  1, Length[less] - 1}]; Take[Sort[d], 55]

PARI

list(lim)=my(v=List(),p=5); forprime(q=7,lim\3+2, if(q-p==2, my(r=3); forprime(s=5,min(lim\p+2,p), if(s-r==2, listput(v, p*r)); r=s)); p=q); Set(v) \\ Charles R Greathouse IV, Oct 21 2022