A358443 - OEIS

%I #43 Apr 16 2023 02:35:27

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

%N 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.

%C 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.

%C 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

%F 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

%e 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.

%e For a(3), every third number after a(2) is also crossed out: 5, 8, 11, ..., which leaves a(3) = 4 next available.

%e For a(4), every fourth number after a(3) is also crossed out: 8, 12, 16, ... which leaves a(4) = 6 next available.

%e For a(5), every fifth number after a(4) is also crossed out: 11, 16, 21, ..., which leaves a(5) = 10 next available.

%K nonn,fini,full

%O 1,2

%A _Tamas Sandor Nagy_ and _Thomas Scheuerle_, Nov 16 2022

%E a(10)-a(11) from _Jon E. Schoenfield_