cp's OEIS Frontend

A264664 a(1)=210; for n > 1, a(n) is the least integer not occurring earlier such that a(n) shares exactly four distinct prime divisors with a(n-1).

%I A264664 #11 Nov 21 2015 22:49:11
%S A264664 210,420,630,840,1050,1260,1470,1680,1890,2100,2310,330,660,990,1320,
%T A264664 1650,1980,2640,2970,3300,3630,3960,4290,390,780,1170,1560,1950,2340,
%U A264664 2730,546,1092,1638,2184,3276,3822,4368,4914,5460,910,1820,3640,4550,6370,7280
%N A264664 a(1)=210; for n > 1, a(n) is the least integer not occurring earlier such that a(n) shares exactly four distinct prime divisors with a(n-1).
%C A264664 The first odd term is a(47) = 1365. - _Michel Marcus_, Nov 21 2015
%H A264664 Michel Lagneau, <a href="/A264664/b264664.txt">Table of n, a(n) for n = 1..2000</a>
%e A264664 630 is in the sequence because the common prime distinct divisors between a(2)=420 and a(3)=630 are 2, 3, 5 and 7.
%p A264664 with(numtheory):a0:={2, 3, 5, 7}:lst:={}:
%p A264664 for n from 1 to 100 do:
%p A264664   ii:=0:
%p A264664     for k from 210 to 50000 while(ii=0) do:
%p A264664       y:=factorset(k):n0:=nops(y):lst1:={}:
%p A264664         for j from 1 to n0 do:
%p A264664         lst1:=lst1 union {y[j]}:
%p A264664         od:
%p A264664          a1:=a0 intersect lst1:
%p A264664          if {k} intersect lst ={} and a1 <> {} and nops(a1)=4
%p A264664           then
%p A264664           printf(`%d, `, k):lst:=lst union {k}:a0:=lst1:ii:=1:
%p A264664          else
%p A264664          fi:
%p A264664       od:
%p A264664   od:
%t A264664 a = {210}; Do[k = 1; While[Nand[! MemberQ[a, k], Length@ Intersection[First /@ FactorInteger@ a[[n - 1]], First /@ FactorInteger@ k] == 4], k++]; AppendTo[a, k], {n, 2, 45}]; a (* _Michael De Vlieger_, Nov 21 2015 *)
%Y A264664 Cf. A246946, A246947.
%K A264664 nonn
%O A264664 1,1
%A A264664 _Michel Lagneau_, Nov 20 2015