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

1,1

Comments

A subsequence of A066509 and offset by one from A176167.

Links

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

Formula

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

Example

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]

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 *)

Prog

(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 */

Crossrefs

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

Sequence in context: A369898 A210017 A176167 * A235854 A203911 A237014

Adjacent sequences: A248200 A248201 A248202 * A248204 A248205 A248206

Keyword

nonn

Author

James G. Merickel, Oct 28 2014

Status

approved