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A096091 Numbers n with property that largest number formed from digits of n (A004186(n)) is divisible by smallest number formed from digits of n (A004185(n)). 5
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 22, 30, 33, 40, 44, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 101, 105, 108, 110, 111, 150, 180, 200, 202, 220, 222, 300, 303, 330, 333, 400, 404, 405, 440, 444, 450, 500, 501, 504, 505, 510, 540, 550, 555, 600, 606 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The number N = d*10^m*(10^k-1)/9 is a member for all m, k where 1 < d < 10, since the quotient is 10^m. E.g., for d = 7, m = 4, k = 8 we get N = 777777770000.
Conjecture: There are infinitely many terms besides these.
From Jon E. Schoenfield, Jul 26 2015: (Start)
Every number whose nonzero digits are all identical (e.g., 70770070777) is a term in the sequence (so the sequence is infinite). Also, if k is a term, then so is k*10 (hence, so is k*10^m for m >= 1). Removal of all terms that satisfy either of the above criteria still leaves an infinite number of terms, beginning with 105, 108, 150, 180, 405, 450, 501, 504, 510, 540, 801, 810, ... (see A260461).
If any integer k is a term, then so is every integer obtained by permuting the digits of k, except for some (not necessarily all) permutations beginning with 0. E.g., since 12000 is a member, so are all the other permutations of its digits that begin with 1 (i.e., 10002, 10020, and 10200), and all those that begin with 2 (i.e., 20001, 20010, 20100, and 21000), as well as the permutations that begin with a single 0 (which, after leading zeros are removed, reduce to 1002, 1020, 1200, 2001, 2010, and 2100), but not those that begin with more than one 0 (i.e., the sequence does not include 12, 21, 102, 120, 201, or 210). Aside from those terms whose nonzero digits are all identical, it appears that only a small number of patterns result from sorting the digits in increasing order (and discarding the zeros, which, of course, are all leading zeros): these "primitives" begin with 12, 15, 16, 18, 24, 25, 36, 45, 48, 125, ... (see A260462). (End)
LINKS
EXAMPLE
110 is a member as 110/011=10.
MAPLE
isA096091 := proc(n)
if modp( A004186(n), A004185(n))= 0 then
true;
else
false;
end if;
end proc:
for n from 1 to 1000 do
if isA096091(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Jul 26 2015
MATHEMATICA
Select[Range[999], (d = Sort@ IntegerDigits@ #; Divisible@@ FromDigits/@ {Reverse@ d, d})&] (* Giovanni Resta, Jul 26 2015 *)
CROSSREFS
Sequence in context: A190220 A113586 A061362 * A084050 A281625 A169824
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Jun 22 2004
EXTENSIONS
Edited, corrected and extended by Robert G. Wilson v, Jun 23 2004
Entry revised by Editors of the OEIS, Jul 26 2015
STATUS
approved

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Last modified May 22 13:22 EDT 2024. Contains 372755 sequences. (Running on oeis4.)