

A358443


a(1) = 1. After each newly determined a(n1), cross out every nth number in the line of the positive integers. a(n) will be the smallest unused number that has not been crossed out.


0



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



FORMULA

For each k exists at least one m ( 0 < m < 12 ), such that (ka(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



KEYWORD

nonn,fini,full


AUTHOR



EXTENSIONS



STATUS

approved



