A061963 - OEIS

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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

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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