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A248203 Numbers n such that n-1, n, and n+1 are the product of 4 distinct primes. 8
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 (list; graph; refs; listen; history; text; internal format)
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: A184455 A210017 A176167 * A235854 A203911 A237014

Adjacent sequences:  A248200 A248201 A248202 * A248204 A248205 A248206

KEYWORD

nonn

AUTHOR

James G. Merickel, Oct 28 2014

STATUS

approved

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Last modified April 15 04:50 EDT 2021. Contains 342975 sequences. (Running on oeis4.)