

A259349


Numbers n such that n1, n, and n+1 are all products of 6 distinct primes.


8



1990586014, 1994837494, 2129658986, 2341714794, 2428906514, 2963553594, 3297066410, 3353808094, 3373085990, 3623442746, 3659230730, 3809238770, 3967387346, 4058711734, 4144727994, 4196154390, 4502893746, 4555267690, 4653623534
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OFFSET

1,1


COMMENTS

A subsequence of A169834.
The rudimentary method employed by the below PARI program reaches the limit of its usefulness here. Contrast it with the method required for A259350, which is over 4.5 orders of magnitude faster than the analog of this (and may still be some distance best).
a(1)=A093550(6) (that sequence's 5th term, with offset 2). The program arbitrarily makes use of this knowledge, but will run (slower) without it.


LINKS

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


EXAMPLE

1990586013 = 3*13*29*67*109*241,
1990586014 = 2*23*37*43*59*461, and
1990586015 = 5*11*17*19*89*1259; and no smaller trio of this kind exists, making the middle value a(1).


PROG

(PARI)
{
\\Program initialized with known a(1).\\
\\The purpose of vector s and value u\\
\\is to skip bad values modulo 36.\\
k=1990586014; s=[4, 4, 8, 8, 8, 4]; u=1;
while(1,
if(issquarefree(k),
if(issquarefree(k1),
if(issquarefree(k+1),
if(omega(k)==6,
if(omega(k1)==6,
if(omega(k+1)==6,
print1(k" ")))))));
k+=s[u]; if(u==6, u=1, u++))
}


CROSSREFS

Cf. A093550, A169834, A248201, A248202, A248203, A248204, A259350, A259801.
Sequence in context: A017615 A232129 A251506 * A204416 A335839 A195225
Adjacent sequences: A259346 A259347 A259348 * A259350 A259351 A259352


KEYWORD

nonn


AUTHOR

James G. Merickel, Jun 24 2015


STATUS

approved



