A337208 -id:A337208 - cp's OEIS frontend

A382167 Repdigit self-numbers that are not in A337208.

3, 5, 7, 9, 222, 88888, 666666, 7777777, 44444444, 555555555, 3333333333, 777777777777, 999999999999, 44444444444444, 222222222222222, 5555555555555555, 333333333333333333, 8888888888888888888, 666666666666666666666, 9999999999999999999999, 77777777777777777777777, 4444444444444444444444444

Offset: 1

N. J. A. Sloane, Mar 26 2025

Shyam Sunder Gupta, On Some Marvellous Numbers of Kaprekar, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 9, 275-315. See Section 9.7.5.

Cf. A003052, A337208.

A336984 Colombian numbers that are also Bogotá numbers.

Original entry on oeis.org

1, 9, 42, 64, 75, 255, 312, 378, 525, 648, 738, 1111, 1278, 2224, 2448, 2784, 2817, 3504, 3864, 3875, 4977, 5238, 5495, 5888, 8992, 9712, 10368, 11358, 11817, 12348, 12875, 13136, 13584, 13775, 13832, 13944, 15351, 15384, 15744, 15900, 16912, 17768, 18095, 19344, 20448

Offset: 1

Bernard Schott, Aug 22 2020

Equivalently, numbers m that are not of the form k + sum of digits of k for any k (A003052), but are of the form q * product of digits of q for some q (A336826).
Repunits are trivially Bogotá numbers but the indices m of the repunits R_m that are Colombian numbers are in A337208. No known prime belongs to this sequence (see A004023).
A336983, A336985, A336986 and this sequence form a partition of the set of positive integers N*.

			42 = 21 * (2*1) is a Bogotá number and there does not exist m < 42 such that 42 = m + sum of digits of m, hence 42 is a Colombian number and 42 is a term.
56 = 14 * (1*4) is a Bogotá number but as 56 = 46 + (4+6), 56 is not a Colombian number, hence 56 is not a term.
648 = 36 * (3*6) = 81 * (8*1) but there does not exist m < 648 such that 648 = m + sum of digits of m, hence 648 is a Colombian number, so 648 is a term that has two different representations as the product of a number and of its decimal digits.

David A. Corneth, Table of n, a(n) for n = 1..10000
Giovanni Resta, Self or Colombian number, Numbers Aplenty.
Puzzling Stackexchange, Pairs of Bogotá Numbers.
Index to sequences related to Colombian numbers.

Intersection of A003052 and A336826.
Cf. A336983 (Bogotá and not Colombian), A336985 (Colombian not Bogotá), A336986 (not Colombian and not Bogotá).
Cf. A336944, A336983, A337208.

m = 21000; Intersection[Complement[Range[m], 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 22 2020 *)

lista(nn) = Vec(setintersect(setminus([1..nn], Set(vector(nn, k, k+sumdigits(k)))), Set(vector(nn, k, k*vecprod(digits(k)))))); \\ Michel Marcus, Aug 23 2020

A337139 Indices m of repunits R_m that are not Colombian (or self) numbers.

Original entry on oeis.org

2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77

Offset: 1

Michel Marcus, Aug 19 2020

Note that 2, 19, 23, 317, 1031, 49081, 86453, 109297, 270343, 5794777, 8177207 (see A004023) are terms. [Last 2 terms added by Serge Batalov, Aug 24 2021]

While all currently known A004023 terms are in this sequence, there is no clear argument that it would hold for all future values. - Serge Batalov, Aug 24 2021

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. A002275 (repunits), A004022 (repunit primes), A004023 (indices of repunit primes), A176995 (not Colombian).

Cf. A337208 (complement).

upto(n)= {my(res = List()); for(i = 1, n, if(is(i), listput(res, i); print1(i", "))); res}
is(n) = {if(n < 8, return(isprime(n))); qd = n; n = 10^n\9; r = 1 + (n-1)%9; h = (r + 9 * (r%2))/2; ld = 10; while(h + 9*qd >= n % ld, ld*=10); vs = qd - valuation(ld, 10); n %= ld; for(i = 0, qd, if(vs + vecsum(digits(n - h - 9*i)) == h + 9*i, return(1))); 0} \\ David A. Corneth, Aug 20 2020

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A382167 Repdigit self-numbers that are not in A337208.

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A336984 Colombian numbers that are also Bogotá numbers.

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A337139 Indices m of repunits R_m that are not Colombian (or self) numbers.

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