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%I #19 Apr 02 2022 09:35:18
%S 2,4,6,11,17,19,23,25,29,37,41,47,49,59,61,67,71,79,83,89,101,103,107,
%T 109,113,131,137,139,149,151,163,167,169,173,179,181,191,193,197,199,
%U 223,227,229,239,251,257,263,269,271,281,283,289,293,311,313,317,331
%N Numbers that are neither Colombian nor Brazilian.
%C The only even terms are 2, 4 and 6 because 2 = 1 + (sum of digits of 1), 4 = 2 + (sum of digits of 2), 6 = 3 + (sum of digits of 3) so these integers are not Colombian then also, because an even number is Brazilian iff it is >= 8.
%C A333858, A336143, A336144 and this sequence form a partition of the set of positive integers N* ( A000027).
%H Giovanni Resta, <a href="http://www.numbersaplenty.com/set/self_number/">Self or Colombian number</a>, Numbers Aplenty.
%H Wikipédia, <a href="https://fr.wikipedia.org/wiki/Nombre_br%C3%A9silien">Nombre brésilien</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>.
%H <a href="/index/Br#Brazilian_numbers">Index to sequences related to Brazilian Numbers</a>.
%H <a href="/index/Coi#Colombian">Index to sequences related to Colombian Numbers</a>.
%e For b = 17, there is no repdigit in some base b < 16 equal to 17, hence 17 is not Brazilian and 17 = 13 + (sum of digits of 13) hence 17 is not Colombian, so 17 is a term.
%t brazQ[n_] := Module[{b = 2, found = False}, While[b < n - 1 && Length[ Union[ IntegerDigits[n, b]]] > 1, b++]; b < n - 1]; n = 300; Select[Union @ Table[Plus @@ IntegerDigits[k] + k, {k, 1, n}], # <= n && !brazQ[#] &] (* _Amiram Eldar_, Jul 17 2020 *)
%Y Intersection of A220570 (not Brazilian) and A176995 (not Colombian).
%Y Cf. A003052 (Colombian), A125134 (Brazilian), A333858 (Brazilian and Colombian), A336143 (Brazilian not Colombian), A336144 (Colombian not Brazilian).
%K nonn,base
%O 1,1
%A _Bernard Schott_, Jul 17 2020
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