A248203 Numbers n such that n-1, n, and n+1 are the product of 4 distinct primes.

203434, 214490, 225070, 258014, 294594, 313054, 315722, 352886, 389390, 409354, 418846, 421630, 452354, 464386, 478906, 485134, 500906, 508046, 508990, 526030, 528410, 538746, 542270, 542794, 548302, 556870, 559690, 569066, 571234, 579886, 582406, 588730

Offset: 1

Author

James G. Merickel, Oct 28 2014

Keywords

• nonn

Comments

A subsequence of A066509 and offset by one from A176167.

Examples

			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]
		

Links

• Anders Hellström, Table of n, a(n) for n = 1..300

Crossrefs

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

Programs

Mathematica

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 *)

PARI

{
\\ Initialized at A093550(4) (3rd term there, w/offset=2). If this \\
\\ program is to run from a different starting value of n, it must not \\
\\ be congruent to -1, 0 or 1 modulo 9 (in addition to being congruent \\
\\ to 2 modulo 4), and either u or the vector s needs to be brought into \\
\\ agreement. \\
n=203434;s=[4,4,8,8,8,4];u=1;
while(1,
  if(issquarefree(n) &&
    issquarefree(n-1) &&
    issquarefree(n+1) &&
    omega(n)==4 &&
    omega(n-1)==4 &&
    omega(n+1)==4,
    print1(n, ", "));
  n+=s[u];if(u==6,u=1,u++))
} \\ James G. Merickel, Jul 23 2015

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));
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 */

Formula

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