A336983 Bogota numbers that are not Colombian numbers.

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

1,1

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).

Links

Table of n, a(n) for n=1..55.

Giovanni Resta, Self or Colombian number, Numbers Aplenty.

Puzzling Stackexchange, Pairs of Bogotá Numbers.

Index to sequences related to Colombian numbers.

Example

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).

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 *)

Prog

(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

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.

Sequence in context: A310560 A156244 A020961 * A005224 A054870 A197567

Adjacent sequences: A336980 A336981 A336982 * A336984 A336985 A336986

Keyword

nonn,base

Author

Bernard Schott, Aug 10 2020

Status

approved