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A309195
a(n) = smallest number missing from A111273 after A111273(n) has been found.
4
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
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
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