A131368 Coprime semiprimes: a(n-1) and a(n) are the closest coprime semiprimes.

4, 9, 10, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 121, 122, 123, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 169, 177, 178, 183, 185, 187, 194, 201, 202, 203

Offset: 1

Author

Zak Seidov, Sep 30 2007

Keywords

• nonn

Comments

The slowest increasing sequence of semiprimes with coprime neighbor terms.

Links

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

Crossrefs

Cf. A051884, A061766, A107621, A109412.

Subsequence of A001358 (semiprimes).

Programs

Maple

A[1]:= 4: t:= 4: count:= 1:
for x from 5 while count < 100 do
  if igcd(x, t) = 1 then
    if numtheory:-bigomega(x)=2 then
      count:= count+1;
      A[count]:= x;
      t:= x;
    fi
  fi
od:
seq(A[i], i=1..100); # Robert Israel, Jun 11 2023

PARI

lista(nn) = {my(vsp = select((x->(bigomega(x) == 2)), vector(nn, k, k)), i = 1, last); while (i <= #vsp, print1(vsp[i], ", "); last = vsp[i]; while(gcd(vsp[i], last) != 1, i++; if (i>#vsp, break)););} \\ Michel Marcus, Jun 25 2019

Formula

gcd(a(n-1), a(n)) = 1.