A291577 a(n) = largest prime factor of a(n-1), or smallest multiple of that factor not yet in the sequence; a(0)=1, a(1)=2.

1, 2, 4, 6, 3, 9, 12, 15, 5, 10, 20, 25, 30, 35, 7, 14, 21, 28, 42, 49, 56, 63, 70, 77, 11, 22, 33, 44, 55, 66, 88, 99, 110, 121, 132, 143, 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 156, 169, 182, 195, 208, 221, 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 238, 255, 272, 289, 306, 323, 19, 38

Offset

0,2

Comments

Serves as a sieve to indicate the appearance of a new prime (at the descents). Primes enter in increasing order.

From Robert G. Wilson v, Sep 04 2017: (Start)

Records: 1, 2, 4, 6, 9, 12, 15, 20, 25, 30, 35, 42, 49, 56, 63, 70, 77, 88, 99, 110, 121, 132, 143, 156, 169, 182, 195, 208, 221, 238, 255, 272, 289, 306, etc.

Where n occurs, or -1 if it does not: 0, 1, 4, 2, 8, 3, 14, -1, 5, 9, 24, 6, 36, 15, 7, -1, 52, -1, 70, 10, 16, 25, 92, -1, 11, 37, -1, 17, 120, 12, 150, -1, 26, 53, 13, -1, 186, 71, 38, -1, 226, 18, 268, 27, -1, 93, 314, -1, 19, -1, etc.

Terms which do not occur: 8, 16, 18, 24, 27, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 81, 84, 90, 96, 98, 100, etc.

If x is a prime power, p^i, which does not appear, then p^j does not appear as well where j > i.

(End)

For n>=1, the number of consecutive terms having prime(n) as greatest prime factor is prime(n+1). - David James Sycamore, Jul 09 2018

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..10000

Example

a(2)=4 since it is the smallest multiple of a(1)=2 not yet in the sequence; a(4)=3 since it is the largest prime factor of a(3)=6.

Mathematica

f[lst_List] := Block[{k = 1, p = FactorInteger[ lst[[-1]]][[-1, 1]]}, While[ MemberQ[lst, k*p], k++]; Append[ lst, k*p]]; Nest[ f, {1}, 71] (* Robert G. Wilson v, Sep 04 2017 *)

Crossrefs

Sequence in context: A122280 A365259 A356851 * A354434 A362842 A338059

Adjacent sequences: A291574 A291575 A291576 * A291578 A291579 A291580

Keyword

nonn

Author

Enrique Navarrete, Aug 30 2017

Status

approved