OFFSET
1,2
COMMENTS
In the first 500000 terms on seventeen occasions the sum of the previous two terms equals the next term, these terms being 3, 5, 8, 11, 100,... ,131072, 262144. It in unknown if there are infinitely many such terms. In the same range there are seventy-three fixed points; see A356017. The sequence is conjectured to be a permutation of the positive integers.
LINKS
Scott R. Shannon, Image of the first 500000 terms. The green line is y = n.
EXAMPLE
a(4) = 5 as a(2) + a(3) = 2 + 3 = 5 which has one prime divisor, and 5 is the smallest unused number that has one prime divisor.
a(6) = 7 as a(4) + a(5) = 5 + 8 = 13 which has one prime divisor, and 7 is the smallest unused number that has one prime divisor.
a(7) = 4 as a(5) + a(6) = 8 + 7 = 15 which has two prime divisors, and 4 is the smallest unused number that has two prime divisors.
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Jul 14 2022
STATUS
approved