A308965 Smallest number not divisible by 10 such that if inserted into itself generates at least n different multiples.

11, 108, 1515, 12195, 102564, 11415525, 108108108, 1219512195, 1219512195, 102564102564, 102564102564, 1012658227848, 121951219512195, 161290322580645, 1176470588235294, 101214574898785425

Offset

1,1

Comments

Multiples of 10 are excluded otherwise the sequence would be equal to A011557, for n>0.

a(6) = 11415525 is the first case where the digits of a(n) are more than n+1.

A011557(n) < a(n) <= 15*A094028(n-2) that is 10^n < a(n) <= 5*(100^(n-1)-1)/33, for n>2. - Giovanni Resta, Jul 04 2019

Here a(8) = a(9) and a(10) = a(11). If we would ask for "exactly" n different multiples then a(8) = 2032520325 and a(10) = 103896103896. - Giovanni Resta, Jul 04 2019

Links

Table of n, a(n) for n=1..16.

Example

a(1) = 11 because 1111/11 = 101;
a(2) = 108 because 110808/108 = 1026 and 101088/108 = 936;
a(5) = 102564 because 110256402564/102564 = 1075001, 101025642564/102564 = 985001, 102102564564/102564 = 995501, 102510256464/102564 = 999476, 102561025644/102564 = 999971.

Maple

P:=proc(q) local a, b, i, j, n, t: for j from 1 to q do
for n from 10^j+1 to q do if n mod 10>0 then b:=length(n):
t:={}: for i from 1 to b-1 do
a:=((trunc(n/10^i)*10^b+n)*10^i+(n mod 10^i))/n:
if frac(a)=0 then t:=t union {a}: fi: od:
if nops(t)>=j then print(n); break: fi: fi: od: od: end: P(10^9);

Crossrefs

Cf. A011557, A094028.

Sequence in context: A193308 A080158 A156935 * A071380 A142423 A159495

Adjacent sequences: A308962 A308963 A308964 * A308966 A308967 A308968

Keyword

base,nonn,more

Author

Paolo P. Lava, Jul 03 2019

Extensions

a(9)-a(16) from Giovanni Resta, Jul 04 2019

Status

approved