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A066509 a(n) is the first of a triple of consecutive integers, each the product of three distinct primes. 13
1309, 1885, 2013, 2665, 3729, 5133, 6061, 6213, 6305, 6477, 6853, 6985, 7257, 7953, 8393, 8533, 8785, 9213, 9453, 9821, 9877, 10281, 10945, 11605, 12453, 12565, 12801, 12857, 12993, 13053, 14133, 14313, 14329, 14465, 14817, 15085, 15265, 15805, 16113, 16133 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A subsequence of A052214 and thus of A005238. - M. F. Hasler, Jan 05 2013

Also, the start of pairs of adjacent sphenic twins, i.e., a(n) = A215217(k) such that A215217(k+1) = A215217(k)+1. Therefore these triples might be called "sphenic triples". They form a subsequence of A242606. - M. F. Hasler, May 18 2014

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

G. L. Honaker, Jr. and C. Caldwell, Prime Curios!

EXAMPLE

a(5) = 3729 because it along with 3730 and 3731 are all the product of three distinct primes.

MATHEMATICA

f[n_]:=Last/@FactorInteger[n]=={1, 1, 1}; lst={}; Do[If[f[n]&&f[n+1]&&f[n+2], AppendTo[lst, n]], {n, 9!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 04 2010 *)

PROG

(PARI) Trip(n) = { local(f); f=factor(n); if (matsize(f)[1] != 3, return(0)); for(i=1, 3, if (f[i, 2] != 1, return(0))); return(1); } { n=0; for (m=1, 10^10, if (!Trip(m) || !Trip(m+1) || !Trip(m+2), next); write("b066509.txt", n++, " ", m); if (n==1000, return) ) } \\ Harry J. Smith, Feb 19 2010

(PARI) A066509(n, show_all=0, a=2*3*5, s=[1, 1, 1]~)={until( !n-- || !a++, until(, factor(a+2)[, 2]!=s && (a+=3) && next; factor(a+1)[, 2]!=s && (a+=2) && next; factor(a)[, 2]==s && break; factor(a+3)[, 2]==s && a++ & break; a+=4); show_all&print1(a", ")); a}  \\ M. F. Hasler, Jan 05 2013

(PARI) is3dp(n)=my(f=factor(n)); matsize(f)==[3, 2]&&vecmax(f[, 2])==1

list(lim)=my(v=List(), t); forprime(p=17, lim\15, forprime(q=7, min(p-1, lim\3), forprime(r=3, min(q-1, lim\(p*q)), t=p*q*r; if(t%4==1 && is3dp(t+1) && is3dp(t+2), listput(v, t))))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jan 05 2013

CROSSREFS

Sequence in context: A209853 A165936 A242606 * A248202 A256668 A205301

Adjacent sequences:  A066506 A066507 A066508 * A066510 A066511 A066512

KEYWORD

nonn

AUTHOR

Jason Earls, Jan 04 2002

STATUS

approved

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Last modified December 8 01:57 EST 2019. Contains 329850 sequences. (Running on oeis4.)