A096089 -id:A096089 - cp's OEIS frontend

A096090 Index of the first occurrence of n in A096089, or 0 if n never appears.

1, 13, 15, 17, 116, 117, 119, 1119, 0, 10, 506, 304, 203, 508, 305, 509, 102, 1012, 307, 205, 308, 2035, 103, 1033, 2056, 207, 1013, 2067, 104, 1044, 209, 1034, 1024, 105, 1055, 1014, 1045, 106, 1035, 2029, 107, 10225, 1046, 1015, 108, 1036, 109, 1078

Offset: 1

Amarnath Murthy, Jun 22 2004

a(9) = 0. For any number with any 0 digits, A096089(n) >= 10. The only number with n digits and no zeros that can be multiplied by 9 to produce a number with the same number of digits is 111...1, so 9 cannot be achieved. A similar argument shows that a(n) = 0 for any n whose leading digit is 9. Note that a(89) = 1011199; probably every number whose leading digit is not 9 does occur in A096089. - Franklin T. Adams-Watters, Jul 19 2006

			a(7) = 119 as floor[911/119] = floor[7.655462184...] = 7 and 119 is the smallest such number.

R. J. Mathar, List of n, a(n) for n=1..1000 with a(n)=-1 for unknown terms.

Cf. A096089, A096091.

1119 from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Jul 19 2004, who remarks that a(9) is not known. The terms after a(9) are 10, 506, 304, 203, 508, 305, 509, 102, 1012, 307, 205, 308, 2035, 103, 1033, 2056, 207, 1013, 2067, 104, 1044, 209, 1034, 1024, 105, 1055, 1014, 1045, 106, 1035, 2029, 107, ...

More terms from Franklin T. Adams-Watters, Jul 19 2006

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)).

Original entry on oeis.org

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

Offset: 1

Amarnath Murthy, Jun 22 2004

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)

			110 is a member as 110/011=10.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A004185, A004186, A096089, A096090, A260461, A260462.

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

Select[Range[999], (d = Sort@ IntegerDigits@ #; Divisible@@ FromDigits/@ {Reverse@ d, d})&] (* Giovanni Resta, Jul 26 2015 *)

Edited, corrected and extended by Robert G. Wilson v, Jun 23 2004

Entry revised by Editors of the OEIS, Jul 26 2015

cp's OEIS Frontend

A096090 Index of the first occurrence of n in A096089, or 0 if n never appears.

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