cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A336143 Integers that are Brazilian and not Colombian.

Original entry on oeis.org

8, 10, 12, 13, 14, 15, 16, 18, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 43, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 73, 74, 76, 77, 78, 80, 81, 82, 84, 85, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100
Offset: 1

Views

Author

Bernard Schott, Jul 10 2020

Keywords

Comments

There are no squares of primes in the data (all squares of primes are not Brazilian except for 121 that is Brazilian, but 121 is Colombian).

Examples

			15 is a term because 15 = 12 + (sum of digits of 12), so 15 is not Colombian and 15 = 33_4, so 15 is Brazilian.

Links

Crossrefs

Intersection of A125134 (Brazilian) and A176995 (not Colombian).
Cf. A003052 (Colombian), A333858 (Brazilian and Colombian), this sequence (Brazilian not Colombian), A336144 (Colombian not Brazilian).

Programs

  • Mathematica
    brazQ[n_] := Module[{b = 2, found = False}, While[b < n - 1 && Length[Union[ IntegerDigits[n, b]]] > 1, b++]; b < n - 1]; n = 100; Select[Union@Table[Plus @@ IntegerDigits[k] + k, {k, 1, n}], # <= n && brazQ[#] &] (* Amiram Eldar, Jul 10 2020 *)

A336144 Integers that are Colombian and not Brazilian.

Original entry on oeis.org

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

Views

Author

Bernard Schott, Jul 14 2020

Keywords

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.

Examples

			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.

Links

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).

Programs

  • 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 *)

A336307 Numbers that are neither Colombian nor Brazilian.

Original entry on oeis.org

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

Views

Author

Bernard Schott, Jul 17 2020

Keywords

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).

Examples

			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.

Links

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).

Programs

  • 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 *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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