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

1,1

Comments

The slowest increasing sequence of semiprimes with coprime neighbor terms.

Links

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

Formula

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

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

Prog

(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

Crossrefs

Cf. A051884, A061766, A107621, A109412.

Subsequence of A001358 (semiprimes).

Sequence in context: A119718 A263648 A051884 * A131457 A072525 A338906

Adjacent sequences: A131365 A131366 A131367 * A131369 A131370 A131371

Keyword

nonn

Author

Zak Seidov, Sep 30 2007

Status

approved