login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A151752 a(n) is the unique n-digit number with all digits odd that is divisible by 5^n. 3
5, 75, 375, 9375, 59375, 359375, 3359375, 93359375, 193359375, 3193359375, 73193359375, 773193359375, 3773193359375, 73773193359375, 773773193359375, 5773773193359375, 15773773193359375, 515773773193359375, 7515773773193359375, 97515773773193359375 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Another way to phrase the proof of uniqueness: after we take the last n-1 digits to be the previous number in the sequence, all odd possibilities for the first digit give different remainders mod 5. By the pigeonhole principle, exactly one of them generates the required number. - Tanya Khovanova, Jun 18 2009
LINKS
33rd USAMO 2003, Problem 1
FORMULA
a(n) = d(n)*10^(n-1) + a(n-1), where d(n), the leading digit of a(n), is one of the odd digits 1, 3, 5, 7, or 9 (forming the complete set of residues modulo 5) and is uniquely defined by the congruence: d(n) == (-a(n-1) / 10^(n-1)) (mod 5). - Max Alekseyev
MAPLE
a:= proc(n) option remember; local k, l;
if n=1 then 5
else l:= a(n-1);
for k from 1 to 9 by 2
while (parse(cat(k, l)) mod 5^n)<>0 do od;
parse(cat(k, l))
fi
end:
seq(a(n), n=1..30); # Alois P. Heinz, Jun 18 2009
MATHEMATICA
nxt[n_]:=Module[{x=FromDigits/@(Prepend[IntegerDigits[n], # ]&/@{1, 3, 5, 7, 9}), l}, l=IntegerLength[n]+1; First[Select[x, Mod[ #, 5^l]==0&]]]; NestList[nxt, 5, 25] (* Harvey P. Dale, Jul 06 2009 *)
PROG
(Magma) v:=[5];
for i in [2..20] do
for s in [1, 3, 5, 7, 9] do
v[i]:=s*10^(i-1)+v[i-1];
if v[i] mod 5^i eq 0 then
break;
end if;
end for;
end for;
v; // Marius A. Burtea, Mar 18 2019
CROSSREFS
Sequence in context: A048350 A030991 A216093 * A127212 A091903 A105490
KEYWORD
nonn,base
AUTHOR
David W. Wilson, Jun 16 2009
EXTENSIONS
More terms from Max Alekseyev, Jun 17 2009
Further terms from Alois P. Heinz, Jun 18 2009
More terms from Harvey P. Dale, Jul 06 2009
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 10:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)