OFFSET

1,2

COMMENTS

As each term must have at least two prime factors no term, other than the initial 2, can be prime.

LINKS

Scott R. Shannon, Image of the terms for n=1..500000. The green line is a(n) = n, indicating the other lines are slightly curved downward.

EXAMPLE

a(4) = 8 as the factors of a(4-2) = a(2) = 2 and a(4-1) = a(3) = 4 = 2*2, thus a(4) must be the minimum unused multiple of 2*2 = 4, which is 8.

a(6) = 6 as the factors of a(6-2) = a(4) = 8 = 2*2*2 and a(6-1) = a(5) = 12 = 2*2*3, thus a(4) must be the minimum unused multiple of 2*2 = 4 or 2*3 = 6. As 4 has been used a(6) = 6.

a(13) = 25 as the factors of a(13-2) = a(11) = 20 = 2*2*5 and a(13-1) = a(12) = 10 = 2*5, thus a(13) must be the minimum unused multiple of 2*2 = 4, 2*5 = 10, or 5*5 = 25. As 4,8,10,12,16,20,24 have been used, a(13) = 25.

CROSSREFS

KEYWORD

nonn

AUTHOR

Scott R. Shannon, Jan 28 2021

STATUS

approved