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

1,2

Comments

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.

Links

Table of n, a(n) for n=1..14.

Index entries for related sequences

Example

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.

Mathematica

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 *)

Prog

(PARI) 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

Crossrefs

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

Sequence in context: A101967 A078590 A358704 * A174603 A062228 A196864

Adjacent sequences: A061960 A061961 A061962 * A061964 A061965 A061966

Keyword

nonn,base,more

Author

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

Extensions

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

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

Status

approved