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.

A336983 Bogota numbers that are not Colombian numbers.

Original entry on oeis.org

4, 11, 16, 24, 25, 36, 39, 49, 56, 81, 88, 93, 96, 111, 119, 138, 144, 164, 171, 192, 224, 242, 250, 297, 336, 339, 366, 393, 408, 422, 448, 456, 488, 497, 516, 520, 522, 564, 575, 696, 704, 744, 755, 777, 792, 795, 819, 848, 884, 900, 912, 933, 944, 966, 992
Offset: 1

Views

Author

Bernard Schott, Aug 10 2020

Keywords

Comments

Equivalently, numbers m that are of the form k + sum of digits of k for some k (A176995), and also of the form q * product of digits of q for some q (A336826).
Repunits are trivially Bogota numbers but the indices m of the repunits R_m that are not Colombian numbers are in A337139; also, all known repunit primes are terms (A004023) [see examples for primes R_2, R_19 and R_23].
35424 is the smallest term that belongs to both A230094 and A336944 (see last example).

Examples

			R_2 = 11 = 10 + (1+0) = 11 * (1*1) is a term;
24 = 21 + (2+1) = 12 * (1*2) is a term;
39 = 33 + (3+3) = 13 * (1*3) is a term;
R_19 = 1111111111111111079 + (16*1+7+9) = 1111111111111111111 * (1^19) hence R_19 is a term;
R_23 = 11111111111111111111077 + (20*1+7+7) = 11111111111111111111111 * (1^23) hence R_23 is a term;
42 = 21 * (2*1) is a Bogota number but there does not exist m < 42 such that 42 = m + sum of digits of m, hence 42 that is also a Colombian number is not a term.
35424 = 35406 + (3+5+4+0+6) = 35397 + (3+5+3+9+7) = 2214 * (2*2*1*4) = 492 * (4*9*2).

Links

Crossrefs

Intersection of A176995 and A336826.
Cf. A003052 (Colombian), A336984 (Bogota and Colombian), A336985 (Colombian not Bogota), A336986 (not Colombian and not Bogota).
Cf. A230093, A230094, A336944, A337139.

Programs

  • Mathematica
    m = 1000; Intersection[Select[Union[Table[n + Plus @@ IntegerDigits[n], {n, 1, m}]], # <= m &], Select[Union[Table[n * Times @@ IntegerDigits[n], {n, 1, m}]], # <= m &]] (* Amiram Eldar, Aug 10 2020 *)
  • PARI
    lista(nn) = Vec(setintersect(Set(vector(nn, k, k+sumdigits(k))), Set(vector(nn, k, k*vecprod(digits(k)))))); \\ Michel Marcus, Aug 20 2020

A336985 Colombian numbers that are not Bogotá numbers.

Original entry on oeis.org

3, 5, 7, 20, 31, 53, 86, 97, 108, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 211, 222, 233, 244, 266, 277, 288, 299, 310, 323, 334, 345, 356, 367, 389, 400, 411, 413, 424, 435, 446, 457, 468, 479, 490, 501, 512, 514, 536, 547, 558, 569, 580, 591, 602, 613
Offset: 1

Views

Author

Bernard Schott, Aug 26 2020

Keywords

Comments

Equivalently, numbers m that are not of the form k + sum of digits of k for any k (A003052), and that are not of the form q * product of digits of q for any q (complement of A336826).
As repunits are trivially Bogotá numbers, there are not repunits in the data.
A336983, A336984, A336986 and this sequence form a partition of the set of positive integers N*

Examples

			7 is a term because there are not k < 7  such that 7 = k + sum of digits of k, and that are not q such that 7 = q * product of digits of q.
13 is not of the form q * product of digits of q for any q <= 13, so 13 is not a Bogotá number, but 13 = 11 + (1+1) is not Colombian, hence 13 is not a term.
42 is Colombian because there does not exist m < 42 such that 42 = m + sum of digits of m, but as 42 = 21 * (2*1) is a Bogota number, 42 is not a term.

Links

Crossrefs

Cf. A003052 (Colombian), A176995 (not Colombian), A336826 (Bogotá numbers), A336983 (Bogotá not Colombian), A336984 (Bogotá and Colombian), this sequence (Colombian not Bogotá), A336986 (not Colombian and not Bogotá).

Programs

  • Mathematica
    m = 600; Intersection[Complement[Range[m], Select[Union[Table[n + Plus @@ IntegerDigits[n], {n, 1, m}]], # <= m &]], Complement[Range[m], Select[Union[Table[n * Times @@ IntegerDigits[n], {n, 1, m}]], # <= m &]]] (* Amiram Eldar, Aug 26 2020 *)
  • PARI
    lista(nn) = Vec(setintersect(setminus([1..nn], Set(vector(nn, k, k+sumdigits(k)))), setminus([1..nn], Set(vector(nn, k, k*vecprod(digits(k))))))); \\ Michel Marcus, Aug 26 2020

A336986 Numbers that are not Colombian and not Bogotá.

Original entry on oeis.org

2, 6, 8, 10, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 26, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85, 87, 89, 90, 91
Offset: 1

Views

Author

Bernard Schott, Aug 22 2020

Keywords

Comments

Equivalently, numbers m that are of the form k + sum of digits of k for some k (A176995), but are not of the form q * product of digits of q for any q.
As repunits are trivially Bogotá numbers, there are not repunits in the data.
A336983, A336984, A336985 and this sequence form a partition of the set of positive integers N*.

Examples

			13 = 11 + (1+1) is not Colombian and 13 is not of the form q * product of digits of q for any q <= 13, so 13 is not a Bogotá number, hence 13 is a term.
39 = 33 + (3+3) is not Colombian but 39 = 13 * (1*3) is a Bogotá number, hence 39 is not a term.
42 = 21 * (2*1) is a Bogotá number but there does not exist k < 42 such that 42 = k + sum of digits of k, hence 42 is a Colombian number and 42 is not a term.

Links

Crossrefs

Cf. A003052 (Colombian), A176995 (not Colombian), A336826 (Bogotá), A336983 (Bogotá and not Colombian), A336984 (Bogotá and Colombian), A336985 (Colombian not Bogotá), this sequence (not Colombian and not Bogotá).

Programs

  • Mathematica
    m = 100; Intersection[Select[Union[Table[n + Plus @@ IntegerDigits[n], {n, 1, m}]], # <= m &], Complement[Range[m], Select[Union[Table[n * Times @@ IntegerDigits[n], {n, 1, m}]], # <= m &]]] (* Amiram Eldar, Aug 22 2020 *)
  • PARI
    lista(nn) = Vec(setintersect(Set(vector(nn, k, k+sumdigits(k))), setminus([1..nn], Set(vector(nn, k, k*vecprod(digits(k))))))); \\ Michel Marcus, Aug 23 2020
Showing 1-3 of 3 results.

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