A246946 a(1)=6; for n > 1, a(n) is the least integer not occurring earlier such that a(n) shares exactly two distinct prime divisors with a(n-1).

6, 12, 18, 24, 30, 10, 20, 40, 50, 60, 15, 45, 75, 90, 36, 42, 14, 28, 56, 70, 35, 105, 21, 63, 84, 48, 54, 66, 22, 44, 88, 110, 55, 165, 33, 99, 132, 72, 78, 26, 52, 104, 130, 65, 195, 39, 117, 156, 96, 102, 34, 68, 136, 170, 80, 100, 120, 108, 114, 38, 76

Offset

1,1

Comments

All terms belong to A024619. Is this a permutation of A024619? - Michel Marcus, Nov 23 2015

Links

Michel Lagneau, Table of n, a(n) for n = 1..2000

Example

18 is in the sequence because the common prime distinct divisors between a(2)=12 and a(3)=18 are 2 and 3.

Maple

with(numtheory):a0:={2, 3}:lst:={}:
for n from 6 to 100 do:
  ii:=0:
    for k from 3 to 50000 while(ii=0) do:
      y:=factorset(k):n0:=nops(y):lst1:={}:
        for j from 1 to n0 do:
        lst1:=lst1 union {y[j]}:
        od:
         a1:=a0 intersect lst1:
         if {k} intersect lst ={} and a1 <> {} and nops(a1)=2
          then
          printf(`%d, `, k):lst:=lst union {k}:a0:=lst1:ii:=1:
         else
         fi:
      od:
  od:

Mathematica

f[s_List]:=Block[{m=s[[-1]], k=6}, While[MemberQ[s, k]||Intersection[Transpose[FactorInteger[k]][[1]], Transpose[FactorInteger[m]][[1]]]=={}|| Length[Intersection[Transpose[FactorInteger[k]][[1]], Transpose[FactorInteger[m]][[1]]]]!=2, k++]; Append[s, k]]; Nest[f, {6}, 71]

Prog

(PARI) lista(nn) = {a = 6; print1(a, ", "); fa = (factor(a)[, 1])~; va = [a]; k = 0; while (k != nn, k = 1; while (!((#setintersect(fa, (factor(k)[, 1])~) == 2) && (! vecsearch(va, k))), k++); a = k; print1(a, ", "); fa = (factor(a)[, 1])~; va = vecsort(concat(va, k)); ); } \\ Michel Marcus, Nov 23 2015

Crossrefs

Cf. A184992, A245481, A246947.

Sequence in context: A315761 A315762 A315763 * A315764 A315765 A315766

Adjacent sequences: A246943 A246944 A246945 * A246947 A246948 A246949

Keyword

nonn

Author

Michel Lagneau, Sep 08 2014

Status

approved