A309195 a(n) = smallest number missing from A111273 after A111273(n) has been found.

2, 2, 4, 4, 4, 4, 6, 8, 8, 8, 8, 8, 8, 8, 10, 10, 10, 10, 12, 12, 12, 12, 16, 16, 16, 16, 16, 16, 16, 16, 24, 26, 26, 26, 26, 26, 26, 26, 28, 28, 28, 28, 28, 28, 28, 28, 28, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 36, 36, 36, 36, 36, 36, 36, 36, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 48, 48

Offset: 1

Author

N. J. A. Sloane, Jul 24 2019

Keywords

• nonn

Comments

A111273(n) can be even only if the triangular number T_n is even, that is when n is congruent to 0 or 3 modulo 4. So, as A111273(4) is not even, for n >= 4 there is an even number k <= n that has not appeared in A111273 by term n, whereas all odd numbers k <= n have appeared (as explained in A111273). Thus a(n) is even for all n. Also a(n) > n/2 for all n >= 1. - Peter Munn, Jul 27 2019

Examples

			1 2 3 4 .5 6 7 8  <- n
1 3 2 5 15 7 4 6  <- A111273
2 2 4 4 .4 4 6 8  <- smallest number missing from A111273 = a(n)
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A111273, A113658, A309196, A309197.

Programs

Maple

N:= 100: # to get a(1)..a(N)
Missing:= {$1..N}:
for n from 1 to N do
  v:= min(numtheory:-divisors(n*(n+1)/2) intersect Missing);
  Missing:= Missing minus {v};
  A[n]:= min(Missing);
od:
seq(A[n],n=1..N); # Robert Israel, Jul 25 2019

Extensions

The values I gave earlier today were wrong, caused by a bug in my program. Thanks to Peter Munn for pointing out that something was wrong. - N. J. A. Sloane, Jul 24 2019