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A248203
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Numbers n such that n-1, n, and n+1 are the product of 4 distinct primes.
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8
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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
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OFFSET
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1,1
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COMMENTS
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A subsequence of A066509 and offset by one from A176167.
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LINKS
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Anders Hellström, Table of n, a(n) for n = 1..300
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FORMULA
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a(n) = A176167(n)+1.
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EXAMPLE
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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]
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MATHEMATICA
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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 *)
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PROG
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(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 */
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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James G. Merickel, Oct 28 2014
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STATUS
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approved
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