A061939 -id:A061939 - cp's OEIS frontend

A029503 Numbers n such that n divides the (right) concatenation of all numbers <= n written in base 10 (most significant digit on right).

1, 2, 3, 5, 6, 9, 101, 107, 153, 167, 277, 414, 486, 858, 1659, 2894, 3093, 4299, 4842, 8838, 22734, 31869, 69492, 361057, 429786, 462018, 859002, 1170801, 1334667, 1663923, 6143512, 6162396, 6212646, 7034661, 8164443

Offset: 1

Olivier Gérard

This sequence differs from A061939 in that all least significant zeros are kept during concatenation.
Right concatenation, reverse order.
No more terms < 10^7. - Lars Blomberg, Oct 06 2011

			n = 22 is not a term since 12345678901112131415161718191021222 is not divisible by 22.
See A029495 for other examples.

Index entries for related sequences

Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

b = 10; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[c, Reverse[IntegerDigits[#, b]]], b], #] &] (* Robert Price, Mar 12 2020 *)

isok(n) = my(s = ""); for (k=1, n, sk = digits(k); forstep (j=#sk, 1, -1, s = concat(s, sk[j]))); (eval(s) % n) == 0; \\ Michel Marcus, Jan 28 2017

Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
Additional comments and more terms from Larry Reeves (larryr(AT)acm.org), May 25 2001
a(25)-a(35) from Lars Blomberg, Oct 06 2011

A240919 Sequence whose n-th term is the sum of the first n digits in the concatenation of the base 10-representation of the sequence.

Original entry on oeis.org

9, 10, 10, 11, 11, 12, 13, 14, 15, 16, 18, 19, 22, 23, 27, 28, 33, 34, 40, 41, 49, 50, 59, 61, 63, 65, 68, 70, 77, 79, 87, 90, 93, 96, 100, 104, 104, 108, 109, 113, 122, 127, 127, 132, 141, 147, 148, 154, 157, 163

Offset: 1

Anthony Zajac, Aug 02 2014

This is the unique sequence in base 10 with this property, aside from the trivial case of beginning this sequence with a(k)=0 for the first k terms.
The only possible nonzero values for a(1) and a(2) are 9 and 10, respectively. This is because a(1) must be a 1-digit number, while a(2) must equal the sum of its own first digit and a(1).
Likewise, for the analogous sequence in a different base b, the first two terms must be b-1 and b.
Essentially the same as A107975. - R. J. Mathar, Jul 07 2023

			a(5) is the sum of the first 5 digits of "91010111112..." = 9 + 1 + 0 + 1 + 0 = 11.

Anthony Zajac, Table of n, a(n) for n = 1..10000

Cf. A004207, A016096, A061939, A065075, A107975.

a240919 = {};
Do[
Which[Length[a240919] <= 0, AppendTo[a240919, 9],
  Length[a240919] == 1,
  AppendTo[a240919,
   First[First[a240919] +
     IntegerDigits[First[Plus[a240919, a240919]]]]],
  True, AppendTo[a240919,
   Total[Take[Flatten[Map[IntegerDigits, a240919]], n]]]], {n,
  10000}]; TableForm[
Transpose[
  List[Range[Length[a240919]],
   a240919]]] (* Michael De Vlieger, Aug 05 2014 *)

lista(nn) = {v = vector(nn); v[1] = 9; v[2] = 10; vd = [9, 1, 0]; print1(v[1], ", ", v[2], ", "); for (n=3, nn, v[n] = sum(k=1, n, vd[k]); vd = concat(vd, digits(v[n])); print1(v[n], ", "););} \\ Michel Marcus, Aug 14 2014

cp's OEIS Frontend

A029503 Numbers n such that n divides the (right) concatenation of all numbers <= n written in base 10 (most significant digit on right).

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