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A066509 a(n) is the first of a triple of consecutive integers, each the product of three distinct primes. 6
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 (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

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 [From 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) ) } [From 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: A233975 A209853 A165936 * A205301 A030646 A223612

Adjacent sequences:  A066506 A066507 A066508 * A066510 A066511 A066512

KEYWORD

nonn

AUTHOR

Jason Earls (zevi_35711(AT)yahoo.com), Jan 04 2002

STATUS

approved

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Last modified April 24 15:13 EDT 2014. Contains 240985 sequences.