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A259349 Numbers n such that n-1, 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 (list; graph; refs; listen; history; text; internal format)
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(k-1),

      if(issquarefree(k+1),

        if(omega(k)==6,

          if(omega(k-1)==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

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Last modified February 26 11:15 EST 2021. Contains 341631 sequences. (Running on oeis4.)