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 A052983 Least multiple of n consisting of a succession of 1's followed by a succession of 0's. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A279992 A287949 A287627 * 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

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Last modified April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)