cp's OEIS Frontend

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

%I A309195 #26 Jul 09 2025 04:47:06
%S A309195 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,
%T A309195 16,16,16,24,26,26,26,26,26,26,26,28,28,28,28,28,28,28,28,28,32,32,32,
%U A309195 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
%N A309195 a(n) = smallest number missing from A111273 after A111273(n) has been found.
%C A309195 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
%H A309195 Robert Israel, <a href="/A309195/b309195.txt">Table of n, a(n) for n = 1..10000</a>
%e A309195 1 2 3 4 .5 6 7 8  <- n
%e A309195 1 3 2 5 15 7 4 6  <- A111273
%e A309195 2 2 4 4 .4 4 6 8  <- smallest number missing from A111273 = a(n)
%p A309195 N:= 100: # to get a(1)..a(N)
%p A309195 Missing:= {$1..N}:
%p A309195 for n from 1 to N do
%p A309195   v:= min(numtheory:-divisors(n*(n+1)/2) intersect Missing);
%p A309195   Missing:= Missing minus {v};
%p A309195   A[n]:= min(Missing);
%p A309195 od:
%p A309195 seq(A[n],n=1..N); # _Robert Israel_, Jul 25 2019
%Y A309195 Cf. A111273, A113658, A309196, A309197.
%K A309195 nonn
%O A309195 1,1
%A A309195 _N. J. A. Sloane_, Jul 24 2019
%E A309195 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