A248203 - OEIS

%I #38 Aug 04 2015 01:11:16

%S 203434,214490,225070,258014,294594,313054,315722,352886,389390,

%T 409354,418846,421630,452354,464386,478906,485134,500906,508046,

%U 508990,526030,528410,538746,542270,542794,548302,556870,559690,569066,571234,579886,582406,588730

%N Numbers n such that n-1, n, and n+1 are the product of 4 distinct primes.

%C A subsequence of A066509 and offset by one from A176167.

%H Anders Hellström, <a href="/A248203/b248203.txt">Table of n, a(n) for n = 1..300</a>

%F a(n) = A176167(n)+1.

%e 203433 factors as 3*19*43*83, 203434 factors as 2*7*11*1321 and 203435 factors as 5*23*29*61; and with no similar smaller trio a(1)=203434. [Corrected by _James G. Merickel_, Jul 23 2015]

%t f1[n_]:=Last/@FactorInteger[n]=={1, 1, 1, 1}; f2[n_]:=Max[Last/@FactorInteger[n]]; lst={}; Do[If[f1[n]&&f1[n + 1]&&f1[n+2], AppendTo[lst, n + 1]], {n, 2 8!, 4 9!}]; lst (* _Vincenzo Librandi_, Aug 02 2015 *)

%o (PARI)

%o {

%o \\ Initialized at A093550(4) (3rd term there, w/offset=2). If this \\

%o \\ program is to run from a different starting value of n, it must not \\

%o \\ be congruent to -1, 0 or 1 modulo 9 (in addition to being congruent \\

%o \\ to 2 modulo 4), and either u or the vector s needs to be brought into \\

%o \\ agreement. \\

%o n=203434;s=[4,4,8,8,8,4];u=1;

%o while(1,

%o   if(issquarefree(n) &&

%o     issquarefree(n-1) &&

%o     issquarefree(n+1) &&

%o     omega(n)==4 &&

%o     omega(n-1)==4 &&

%o     omega(n+1)==4,

%o     print1(n, ", "));

%o   n+=s[u];if(u==6,u=1,u++))

%o } \\ _James G. Merickel_, Jul 23 2015

%o (PARI) is_ok(n)=(n>1&&omega(n-1)==4&&omega(n)==4&&omega(n+1)==4&&issquarefree(n-1)&&issquarefree(n)&&issquarefree(n+1));

%o first(m)=my(v=vector(m),i,t=2);for(i=1,m,while(!is_ok(t),t++);v[i]=t;t++);v; /* _Anders Hellström_, Aug 01 2015 */

%Y Cf. A066509, A176167, A248201, A248202, A248204, A259349, A259350, A259801.

%K nonn

%O 1,1

%A _James G. Merickel_, Oct 28 2014