A358443 a(1) = 1. After each newly determined a(n-1), cross out every n-th number in the line of the positive integers. a(n) will be the smallest unused number that has not been crossed out.

1, 2, 4, 6, 10, 18, 30, 42, 90, 138, 162

Offset

1,2

Comments

This sequence is generated by a sieve. Its first term is odd, and the rest are even numbers. Since every remaining number is crossed out after a(11) is determined, the sequence is finite, having only 11 terms.

Consider hyperplanes with eleven dimensions and a normal vector N = {2, 3, ..., 12} and with distances to the origin |(k+162)|/|N| and k is an integer. We will find at least one point with only integer coordinates for each of these distances located on such a hyperplane. If k is positive then a hyperplane exists where such a point has only positive coordinates. - Thomas Scheuerle, Nov 17 2022

Links

Table of n, a(n) for n=1..11.

Formula

For each k exists at least one m ( 0 < m < 12 ), such that (k-a(m)) mod (m+1) = 0. - Thomas Scheuerle, Nov 17 2022

Example

For a(2), after a(1) = 1 every second number is crossed out: 3, 5, 7, 9, 11, ..., which leaves a(2) = 2 next available.
For a(3), every third number after a(2) is also crossed out: 5, 8, 11, ..., which leaves a(3) = 4 next available.
For a(4), every fourth number after a(3) is also crossed out: 8, 12, 16, ... which leaves a(4) = 6 next available.
For a(5), every fifth number after a(4) is also crossed out: 11, 16, 21, ..., which leaves a(5) = 10 next available.

Crossrefs

Sequence in context: A025052 A142584 A098197 * A175941 A317536 A203175

Adjacent sequences: A358440 A358441 A358442 * A358444 A358445 A358446

Keyword

nonn,fini,full

Author

Tamas Sandor Nagy and Thomas Scheuerle, Nov 16 2022

Extensions

a(10)-a(11) from Jon E. Schoenfield

Status

approved