A333858 Numbers that are both Colombian and Brazilian.

7, 20, 31, 42, 64, 75, 86, 108, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 211, 222, 244, 255, 266, 288, 299, 310, 312, 323, 334, 345, 356, 378, 400, 411, 413, 424, 435, 446, 468, 490, 501, 512, 514, 525, 536, 558, 580, 591, 602, 615, 626, 637, 648, 670, 681, 692

Offset: 1

Author

Bernard Schott, Apr 08 2020

Keywords

• nonn
• base

Comments

121 is the only square of prime in this sequence.

Examples

			20 is a term because it is not of the form m + sum of digits of m for any m < 20, so 20 is Colombian and 20 = (22)_9, so 20 is also Brazilian.
		

Links

• Wikipédia, Nombre brésilien (in French).
• Index entries for sequences related to Brazilian Numbers.
• Index entries for sequences related to Colombian Numbers.

Crossrefs

Intersection of A003052 and A125134.

Programs

Mathematica

brazQ[n_] := Module[{b = 2, found = False}, While[b < n - 1 && Length[Union[IntegerDigits[n, b]]] > 1, b++]; b < n - 1]; n = 700; Select[Complement[Range[n], Union @ Table[Plus @@ IntegerDigits[k] + k, {k, 1, n}]], brazQ] (* Amiram Eldar, Apr 08 2020 after T. D. Noe at A125134 *)