1,1

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

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

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)

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

Cf. A111273, A113658, A309196, A309197.

Sequence in context: A098667 A279506 A105678 * A367026 A028397 A053644

Adjacent sequences: A309192 A309193 A309194 * A309196 A309197 A309198

N. J. A. Sloane, Jul 24 2019

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

approved