A362015 - OEIS

A362015

a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that, given the list of primes that form the factors of all previous terms a(1)..a(n-1), is a multiple of the prime in that list which is a factor of the fewest previous terms. If two or more such primes exist the smallest is chosen.

1, 2, 4, 6, 3, 9, 8, 12, 15, 5, 10, 20, 25, 18, 30, 35, 7, 14, 21, 28, 42, 49, 40, 56, 45, 63, 50, 70, 77, 11, 22, 33, 44, 55, 66, 88, 99, 110, 121, 84, 132, 91, 13, 26, 39, 52, 65, 78, 104, 117, 130, 143, 156, 169, 98, 154, 182, 165, 195, 176, 208, 105, 187, 17, 34, 51, 68, 85, 102, 119, 136

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

After 5 million terms the lowest number not to have appeared is 16 = 2^4. In that range 2 is a factor of 2614180 terms while 3 is a factor of 1763610 terms. As these are the most and second-most common prime factors this suggest that 16, and other higher powers of 2, will never appear as that would require 2 to be the least common factor of all previous terms. This is also true for the powers of the other smaller primes.

In the first 5 million terms the only fixed point, other than the first two terms, is 4175, although it is probable that more exist.

LINKS

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Scott R. Shannon, Image of the first 100000 terms. The green line is a(n) = n.

Scott R. Shannon, Image of the first 5000000 terms

EXAMPLE

a(5) = 3 as the list of primes that divide all previous terms a(1)..a(4) is 2 and 3, with 2 being a factor of three terms and 3 being a factor of one term. Therefore a(5) is the lowest multiple of 3 that has not appeared, which is 3.

CROSSREFS

Cf. A361372, A351495, A359804, A353026, A352793.

Sequence in context: A207779 A338338 A350927 * A374284 A391057 A096665

Adjacent sequences: A362012 A362013 A362014 * A362016 A362017 A362018

KEYWORD

nonn,look

AUTHOR

Scott R. Shannon, Apr 03 2023

STATUS

approved