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A248201 Numbers n such that n-1, n and n+1 are all squarefree semiprimes. 8
34, 86, 94, 142, 202, 214, 218, 302, 394, 446, 634, 698, 922, 1042, 1138, 1262, 1346, 1402, 1642, 1762, 1838, 1894, 1942, 1982, 2102, 2182, 2218, 2306, 2362, 2434, 2462, 2518, 2642, 2722, 2734, 3098, 3386, 3602, 3694, 3866, 3902, 3958, 4286, 4414 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A subsequence of A169834. - M. F. Hasler, Oct 26 2014

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000

Wikipedia, Semiprime

FORMULA

a(n) = A039833(n) + 1. - Michel Marcus, Oct 25 2014

EXAMPLE

33, 34 and 35 factor as 3*11, 2*17 and 5*7, respectively.  No smaller such trio exists, so a(1)=34.

MATHEMATICA

lst={}; Do[z=n^3 + 3 n^2 + 2 n; If[PrimeOmega[z/n]==PrimeOmega[z/(n + 2)]==4 && PrimeNu[z]==6, AppendTo[lst, n + 1]], {n, 1, 6000, 2}]; lst (* Vincenzo Librandi, Jul 24 2015 *)

SequencePosition[Table[If[SquareFreeQ[n]&&PrimeOmega[n]==2, 1, 0], {n, 4500}], {1, 1, 1}][[All, 1]]+1 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 11 2018 *)

PROG

(PARI) sq(n)=bigomega(n)==2 && omega(n)==2;

for(n=3, 10^4, if(sq(n-1)&&sq(n)&&sq(n+1), print1(n, ", ")));

\\ Joerg Arndt, Oct 18 2014

CROSSREFS

Cf. A039833, A169834, A006881, A248202, A248203, A248204, A259349, A259350, A259801.

Sequence in context: A213025 A086005 A169834 * A140602 A067977 A183311

Adjacent sequences:  A248198 A248199 A248200 * A248202 A248203 A248204

KEYWORD

nonn

AUTHOR

James G. Merickel, Oct 03 2014

STATUS

approved

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Last modified September 20 12:29 EDT 2019. Contains 327231 sequences. (Running on oeis4.)