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A299442 Lexicographically earliest sequence of distinct positive terms such that, for any n > 1, if prime(k) is the greatest prime factor of a(n) then k divides a(n+1) (where prime(k) denotes the k-th prime). 3
1, 2, 3, 4, 5, 6, 8, 7, 12, 10, 9, 14, 16, 11, 15, 18, 20, 21, 24, 22, 25, 27, 26, 30, 33, 35, 28, 32, 13, 36, 34, 42, 40, 39, 48, 38, 56, 44, 45, 51, 49, 52, 54, 46, 63, 60, 57, 64, 17, 70, 68, 77, 50, 66, 55, 65, 72, 58, 80, 69, 81, 62, 88, 75, 78, 84, 76 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In other words, for any n > 1, A061395(a(n)) divides a(n+1).

See also A299441 for the variant involving least prime factors.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A299442

Rémy Sigrist, Colored scatterplot of the first 100000 terms (where the color is function of A006530(a(n-1)))

EXAMPLE

The first terms, alongside A061395(a(n)), are:

  n     a(n)    A061395(a(n))

  --    ----    -------------

   1       1       0

   2       2       1

   3       3       2

   4       4       1

   5       5       3

   6       6       2

   7       8       1

   8       7       4

   9      12       2

  10      10       3

  11       9       2

  12      14       4

  13      16       1

  14      11       5

  15      15       3

  16      18       2

  17      20       3

  18      21       4

  19      24       2

  20      22       5

MAPLE

N:= 1000: # to get terms before the first term > N

with(numtheory):

V:= Vector(N):

A[1]:= 1: A[2]:= 2: V[1]:= 1: V[2]:= 1:

found:= true:

for n from 2 while found do

     found:= false;

     k:= pi(max(factorset(A[n])));

     for v from k to N by k do

       if V[v] = 0 then

         V[v]:= 1;

         A[n+1]:= v;

         found:= true;

         break

       fi

     od

od:

seq(A[i], i=1..n-1); # Robert Israel, Feb 18 2018

MATHEMATICA

max = 100; Clear[a, V]; a[_] = 0; V[_] = 0; a[1] = 1; a[2] = 2; V[1] = 1; V[2] = 1; found = True; For[n = 2, found, n++, found = False; k = PrimePi[ FactorInteger[a[n]][[-1, 1]]]; For[v = k, v <= max, v += k, If[V[v] == 0, V[v] = 1; a[n+1] = v; found = True; Break[]]]]; DeleteCases[ Array[a, max], 0] (* Jean-François Alcover, Feb 23 2018, after Robert Israel *)

PROG

(PARI) See Links section.

CROSSREFS

Cf. A006530, A061395, A299441.

Sequence in context: A232895 A274607 A262374 * A299440 A145518 A256221

Adjacent sequences:  A299439 A299440 A299441 * A299443 A299444 A299445

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Feb 10 2018

STATUS

approved

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Last modified November 19 04:39 EST 2018. Contains 317333 sequences. (Running on oeis4.)