A336144 Integers that are Colombian and not Brazilian.

1, 3, 5, 9, 53, 97, 233, 277, 367, 389, 457, 479, 547, 569, 613, 659, 727, 839, 883, 929, 1021, 1087, 1109, 1223, 1289, 1447, 1559, 1627, 1693, 1783, 1873, 2099, 2213, 2347, 2437, 2459, 2503, 2549, 2593, 2617, 2683, 2729, 2819, 2953, 3023, 3067, 3089, 3313, 3359

Offset

1,2

Comments

There are no even terms because 2, 4 and 6 are not Colombian as 2 = 1 + (sum of digits of 1), 4 = 2 + (sum of digits of 2) and 6 = 3 + (sum of digits of 3), then every even integer >= 8 is Brazilian.

Links

Table of n, a(n) for n=1..49.

Giovanni Resta, Self or Colombian number, Numbers Aplenty.

Wikipédia, Nombre brésilien (in French).

Index to sequences related to Colombian Numbers.

Index to sequences related to Brazilian Numbers.

Example

233 is a term because 233 is not of the form m + (sum of digits of m) for any m < 233, so 233 is Colombian and there is no Brazilian representation for 233.

Mathematica

brazQ[n_] := Module[{b = 2, found = False}, While[b < n - 1 && Length[Union[IntegerDigits[n, b]]] > 1, b++]; b < n - 1]; n = 4000; Select[Complement[Range[n], Union @ Table[Plus @@ IntegerDigits[k] + k, {k, 1, n}]], !brazQ[#] &] (* Amiram Eldar, Jul 14 2020 *)

Crossrefs

Intersection of A003052 (Colombian) and A220570 (non-Brazilian).

Cf. A125134 (Brazilian), A333858 (Brazilian and Colombian), A336143 (Brazilian and not Colombian), this sequence (Colombian and not Brazilian).

Sequence in context: A125708 A055289 A124974 * A215440 A163550 A123220

Adjacent sequences: A336141 A336142 A336143 * A336145 A336146 A336147

Keyword

nonn,base

Author

Bernard Schott, Jul 14 2020

Status

approved