A029503 -id:A029503 - cp's OEIS frontend

A061939 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, 99, 153, 189, 238, 252, 323, 444, 539, 927, 3099, 3753, 4224, 5451, 8967, 44544, 53673, 97119, 1423719, 3860793, 4773591

Offset: 1

Larry Reeves (larryr(AT)acm.org), May 24 2001

This sequence differs from A029503 in that all least significant zeros are removed before concatenation.

No more terms < 10^7. - Lars Blomberg, Oct 20 2011

			See A061931 for example.

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, IntegerDigits[IntegerReverse[#, b], b]], b], #] &] (* Robert Price, Mar 08 2020 *)

lista(nn, m=10) = my(s, t); for(k=1, nn, s=k/m^valuation(k, m); while(s, t=t*m+s%m; s\=m); if(t%k==0, print1(k, ", "))); \\ Jinyuan Wang, Dec 05 2020

Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002

a(24)-a(26) from Lars Blomberg, Oct 20 2011

A281190 Concatenation of the reversed digits of numbers from 1 to n, mod n.

Original entry on oeis.org

0, 0, 0, 2, 0, 0, 5, 6, 0, 1, 6, 9, 3, 1, 6, 9, 5, 9, 1, 2, 18, 6, 12, 18, 2, 6, 18, 26, 7, 3, 20, 27, 6, 3, 28, 27, 7, 19, 12, 24, 4, 24, 12, 28, 9, 8, 42, 12, 22, 5, 3, 45, 41, 45, 50, 45, 45, 23, 16, 6, 6, 54, 27, 30, 61, 6, 37, 30, 21, 67, 47, 63, 52, 67, 57, 19, 28, 15, 58, 28, 72, 22, 56, 24, 83, 34, 3, 72, 72, 9, 85, 69, 57

Offset: 1

Robert G. Wilson v, Jan 16 2017

Note that leading zeros are not omitted when numbers are reversed. - N. J. A. Sloane, Jan 23 2017

			a(13) = A138957(13) mod 13 == 12345678901112131 mod 13 == 3.

Indranil Ghosh, Table of n, a(n) for n = 1..20008

Cf. A029503, A095221, A114795, A138957, A281066.

f[n_] := Mod[ Fold[#1*10^IntegerLength@#2 + FromDigits@ Reverse@ IntegerDigits@#2 &, 0, Range@ n], n]; Array[f, 105]

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

def A281190(n):
    s=""
    for i in range(1,n+1):
        s+=str(i)[::-1]
    return int(s)%n # Indranil Ghosh, Jan 28 2017

a(n) = A138957(n) mod n.

cp's OEIS Frontend

A061939 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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