|
| |
|
|
A308965
|
|
Smallest number not divisible by 10 such that if inserted into itself generates at least n different multiples.
|
|
0
|
|
|
|
11, 108, 1515, 12195, 102564, 11415525, 108108108, 1219512195, 1219512195, 102564102564, 102564102564, 1012658227848, 121951219512195, 161290322580645, 1176470588235294, 101214574898785425
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
