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A336144
Integers that are Colombian and not Brazilian.
2
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.
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
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Jul 14 2020
STATUS
approved