A029527 -id:A029527 - cp's OEIS frontend

A061963 Numbers n such that n divides the (left) concatenation of all numbers <= n written in base 10 (most significant digit on right).

1, 3, 9, 189, 753, 987, 6739, 10953, 51963, 171897, 224081, 635031, 1135001, 4437459

Offset: 1

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

This sequence differs from A029527 in that all least significant zeros are kept during concatenation.
Left concatenation, reverse order (i.e., digit-wise reversal of the concatenation 123...n), as in A138793.
No more terms < 10^7.
All terms must be odd.

			n = 13 is not a term since 31211101987654321 is not divisible by 13. (Note that the order of the digits of 13, 12 and 10 is reversed.)
See A061955 for further examples.

Index entries for related sequences

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

Cf. A138793.

k = 2; lst = {}; rid = 1; While[k < 1001, exp = Floor[ Log10[rid]] + 1 + If[Mod[k, 10] == 1, IntegerExponent[k - 1, 10], 0]; rid = rid + FromDigits@ Reverse@ IntegerDigits@ k*(10^exp); If[ Mod[rid, k] == 0, Print@ k; AppendTo[lst,k]]; k++]; lst (* and to test any single value n *) fQ[n_] := Mod[ FromDigits@ Reverse@ Flatten@ IntegerDigits@ Range@ n, n] == 0 (* Robert G. Wilson v, Sep 12 2011 *)
Select[Range[5*10^6],Divisible[FromDigits[Reverse[Flatten[ IntegerDigits/@ Range[ #]]]], #]&] (* Harvey P. Dale, Apr 10 2017 *)

isok(n) = my(s = ""); forstep (k=n, 1, -1, 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

a(12)-a(14) from Lars Blomberg, Aug 19 2011

cp's OEIS Frontend

A061963 Numbers n such that n divides the (left) concatenation of all numbers <= n written in base 10 (most significant digit on right).

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