OFFSET
1,2
COMMENTS
The majority of terms are concentrated along a line of gradient ~1.07, but occasional large drops in value appear which may contain prime values. These primes can force the following term to be somewhat larger than the main line of concentration.
Overall the primes are rare, only 171 terms being prime in the first 10^8 terms, see A394414, and they do not occur in their natural order. In this range the smallest missing prime is 17, although given the pattern of the large drops in value it is conjectured eventually all numbers will appear.
In the first 10^8 terms the only fixed points are 1, 2, 8, 55, and 1243117, although more likely exist.
LINKS
Scott R. Shannon, Table of n, a(n) for n = 1..10000
Scott R. Shannon, Image of the first 100000 terms. The colors are graduated across the spectrum from red to violet to show the total number of prime factors of each term, counted with multiplicity. The thin green line is a(n) = n.
Scott R. Shannon, Image of the first 100000000 terms.
EXAMPLE
a(14) = 16 as 16 is unused, shares a factor with a(13) = 14, and is only 2 away from a(12) = 18. This is the first term to differ from A064413. Note that 20 also satisfies these same criteria, but the smaller of the two possible values is chosen.
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Scott R. Shannon, Mar 20 2026
STATUS
approved
