A240911 Smallest number greater than a(n-1) divisible by smallest number that is not a divisor of a(n-1).

1, 2, 3, 4, 6, 8, 9, 10, 12, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 36, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 63, 64, 66, 68, 69, 70, 72, 75, 76, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 92, 93, 94, 96, 100

Offset

1,2

Comments

Conjecture: Numbers that are not in this sequence below any finite limit will never outnumber numbers that are.

That is, a(n) < 2n for all n. This holds for n < 10^10. - Charles R Greathouse IV, Apr 14 2014

The expected value of the first differences of this sequence is Sum_{q>=2} (q(p-1)/(2*lcm(2,...,q)) as q = p^k ranges over the prime powers, or approximately 1.39389022808623327303..., so the conjecture is very likely to be true. - Charlie Neder, Apr 26 2019

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

a(5) cannot be 5 because smallest number that is not a divisor of 4 is 3 and 3 is not a divisor of 5.

Prog

(PARI) step(n)=for(k=2, n+1, if(n%k, return((n\k+1)*k)))
v=vector(100); v[1]=1; for(n=2, #v, v[n]=step(v[n-1])); v \\ Charles R Greathouse IV, Apr 14 2014

Crossrefs

Sequence in context: A263079 A362077 A085451 * A064150 A259227 A196149

Adjacent sequences: A240908 A240909 A240910 * A240912 A240913 A240914

Keyword

nonn,easy

Author

J. Lowell, Apr 14 2014

Extensions

a(26)-a(63) from Charles R Greathouse IV, Apr 14 2014

Status

approved