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

1,1

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

Links

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

Example

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)

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

Crossrefs

Cf. A111273, A113658, A309196, A309197.

Sequence in context: A098667 A279506 A105678 * A367026 A028397 A053644

Adjacent sequences: A309192 A309193 A309194 * A309196 A309197 A309198

Keyword

nonn

Author

N. J. A. Sloane, Jul 24 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

Status

approved