A052983 Least multiple of n consisting of a succession of 1's followed by a succession of 0's.

10, 10, 1110, 100, 10, 1110, 1111110, 1000, 1111111110, 10, 110, 11100, 1111110, 1111110, 1110, 10000, 11111111111111110, 1111111110, 1111111111111111110, 100, 1111110, 110, 11111111111111111111110, 111000, 100, 1111110, 1111111111111111111111111110

Offset

1,1

Comments

All entries are differences of two terms of A000042. Since the pigeonhole principle guarantees that, for any m, two among the first m+1 entries of A000042 are congruent modulo m, their difference (i.e. belonging to this sequence) is therefore divisible by m, so that such numbers exist for all m. This sequence is thus infinite.

For n>1, a(n) consists of s 1's and t 0's, where s=A084681(X) and t is the greater of p or q (s=1 for X=1, t=1 for p=q=0), when we write n=X*Y with (X,Y)=1 and Y=2^p*5^q.

Links

Table of n, a(n) for n=1..27.

Formula

a(n) = A276348(n) * n; A227362(a(n)) = 10. - Jaroslav Krizek, Aug 30 2016

Example

We have a(6)=1110 because 6 divides 1110=6*185, the smallest such one with a string of 1's followed by that of 0's

Mathematica

f[n_] := Select[ Map[ FromDigits, IntegerDigits[ Table[ Sum[2^i, {i, k, j, -1}], {j, k, 1, -1}], 2]]/n, IntegerQ[ # ] & ]; g[n_] := Block[{k = 1}, While[ f[n] == {}, k++ ]; n*Min[ f[n]]]; Table[ g[n], {n, 1, 27}]
nn=30; With[{nos=Sort[Flatten[Table[FromDigits[Join[Table[1, {n}], Table[ 0, {i}]]], {n, nn}, {i, 5}]]]}, Flatten[Table[Select[nos, Divisible[#, n]&, 1], {n, nn}]]] (* Harvey P. Dale, Mar 09 2014 *)

Crossrefs

Cf. A000042, A002371, A007732.

Cf. A084681.

Sequence in context: A287949 A287627 A364773 * A072804 A079793 A086884

Adjacent sequences: A052980 A052981 A052982 * A052984 A052985 A052986

Keyword

base,nonn

Author

Lekraj Beedassy, Jun 26 2003

Extensions

Edited, corrected and extended by Robert G. Wilson v, Jun 26 2003

Status

approved