A336307 Numbers that are neither Colombian nor Brazilian.

2, 4, 6, 11, 17, 19, 23, 25, 29, 37, 41, 47, 49, 59, 61, 67, 71, 79, 83, 89, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 223, 227, 229, 239, 251, 257, 263, 269, 271, 281, 283, 289, 293, 311, 313, 317, 331

Offset

1,1

Comments

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.

A333858, A336143, A336144 and this sequence form a partition of the set of positive integers N* ( A000027).

Links

Table of n, a(n) for n=1..57.

Giovanni Resta, Self or Colombian number, Numbers Aplenty.

Wikipédia, Nombre brésilien.

Wikipedia, Partition of a set.

Index to sequences related to Brazilian Numbers.

Index to sequences related to Colombian Numbers.

Example

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.

Mathematica

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 *)

Crossrefs

Intersection of A220570 (not Brazilian) and A176995 (not Colombian).

Cf. A003052 (Colombian), A125134 (Brazilian), A333858 (Brazilian and Colombian), A336143 (Brazilian not Colombian), A336144 (Colombian not Brazilian).

Sequence in context: A094719 A294811 A333162 * A336134 A255214 A222047

Adjacent sequences: A336304 A336305 A336306 * A336308 A336309 A336310

Keyword

nonn,base

Author

Bernard Schott, Jul 17 2020

Status

approved