A276348 a(n) = the smallest number k such that k*n is a number with a string of 1's followed by a string of 0's.

10, 5, 370, 25, 2, 185, 158730, 125, 123456790, 1, 10, 925, 85470, 79365, 74, 625, 653594771241830, 61728395, 58479532163742690, 5, 52910, 5, 483091787439613526570, 4625, 4, 42735, 41152263374485596707818930, 396825, 383141762452107279693486590, 37

Offset

1,1

Comments

a(n) = the smallest number k such that k*n is a number from A276349.

a(n) > 0 for all n.

References

L. Pick, Dirichletovy šuplíčky. Pokroky matematiky, fyziky & astronomie; 2 (2016), 106-118. (In Czech; The Dirichlet pigeonhole principle)

Links

Robert Israel, Table of n, a(n) for n = 1..1016

Formula

a(n) = A052983(n)/n.

From Robert Israel, Aug 30 2016: (Start)

Let n = 2^b*5^c*m where GCD(m,10)=1, and q = A084680(9*m).

If b=c=0 let d=1, otherwise d=max(b,c).

Then a(n) = 2^(d-a)*5^(d-b)*(10^q-1)/(9*m). (End)

Example

For n=3; 3*370 = 1110 (term of A276349).

Maple

f:= proc(n) local b, c, d, m, q;
    b:= padic:-ordp(n, 2); c:= padic:-ordp(n, 5); if b+c=0 then d:= 1 else d:= max(b, c) fi; m:= n/2^b/5^c; q:= numtheory:-order(10, 9*m);
     2^(d-b)*5^(d-c)*(10^q-1)/(9*m)
end proc:
map(f, [$1..100]); # Robert Israel, Aug 30 2016

Mathematica

Table[k = 1; While[! If[Length@ # == 2, Flatten@ Map[Union, #] == {1, 0}, False] &@ Split@ IntegerDigits[k n], k++]; k, {n, 8}] (* Michael De Vlieger, Aug 30 2016 *)

Prog

(Magma) a:=10; S:=[a]; for n in [2..6] do k:=0; flag:= true; while flag do k+:=1; if [k*n] subset [n: n in [1..10000] | Seqint(Setseq(Set(Sort(Intseq(n))))) eq 10 and Seqint(Sort((Intseq(n)))) eq n] then Append(~S, k); a:=k; flag:=false; end if; end while; end for; S;

Crossrefs

Cf. A052983, A084680, A276349.

Sequence in context: A094260 A239603 A241439 * A281400 A283726 A370388

Adjacent sequences: A276345 A276346 A276347 * A276349 A276350 A276351

Keyword

nonn,base

Author

Jaroslav Krizek, Aug 30 2016

Status

approved