A223475 -id:A223475 - cp's OEIS frontend

A223474 Least positive multiple of n that when written in base 10 has digits in nonincreasing order.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 60, 52, 42, 30, 32, 51, 54, 76, 20, 21, 22, 92, 72, 50, 52, 54, 84, 87, 30, 31, 32, 33, 442, 70, 72, 74, 76, 663, 40, 41, 42, 43, 44, 90, 92, 94, 96, 98, 50, 51, 52, 53, 54, 55, 840, 741, 522, 531, 60, 61, 62, 63, 64, 65, 66, 871, 544, 552, 70, 71, 72, 73, 74, 75, 76, 77, 6552, 553, 80, 81, 82, 83, 84, 85

Offset: 1

Paul Tek, Mar 20 2013

This sequence is well defined (same reasoning as for A079339).

			a(39) = 663 because it is the least multiple of 39 appearing in A009996.

Giovanni Resta, Table of n, a(n) for n = 1..2000

a(n)/n yields sequence A223475.
Cf. A004290, A181060.
Cf. A009996.

a[n_] := Block[{x=n}, While[0 < Max@Differences@IntegerDigits@x, x += n]; x]; Array[a, 85] (* Giovanni Resta, Mar 26 2013 *)

sub A223474 {
    my $n = shift;
    my $a = $n;
    while ($a !~ /^9*8*7*6*5*4*3*2*1*0*$/) {
        $a += $n;
    }
    return $a;
}
foreach (1..100) {
    print A223474($_), ",";
}

A381770 a(n) is the least k > 0 such that the factorial base expansion of k*n has digits in nonincreasing order.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 5, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 6, 3, 2, 2, 3, 1, 2, 1, 1, 3, 3, 2, 3, 3, 2, 2, 14, 2, 2, 2, 2, 2, 2, 1, 6, 3, 2, 2, 8, 1, 2, 1, 1, 2, 2, 1, 5, 1, 1, 1, 1, 4, 8, 4, 6, 6, 8, 1, 6, 4, 2, 2, 9, 1, 8, 1, 1, 7, 8, 1, 5, 1

Offset: 0

Rémy Sigrist, Mar 07 2025

The sequence is well defined as for any n > 0, the factorial base expansion of n! has digits in nonincreasing order.

			The first terms, alongside the factorial base expansion of n*a(n), are:
  n   a(n)  fact(n*a(n))
  --  ----  ------------
   0     1  0
   1     1  1
   2     1  1,0
   3     1  1,1
   4     1  2,0
   5     1  2,1
   6     1  1,0,0
   7     2  2,1,0
   8     1  1,1,0
   9     1  1,1,1
  10     2  3,1,0
  11     2  3,2,0
  12     1  2,0,0
  13     5  2,2,2,1
  14     1  2,1,0
  15     1  2,1,1

Cf. A223475, A351987, A381771.

is(n) = { my (p = -1); for (r = 2, oo, if (n==0, return (1), p > p = n%r, return
 (0)); n \= r;); }
a(n) = { for (k = 1, oo, if (is(k*n), return (k););); }

from itertools import count
def facbase(n, i=2): return [n] if n < i else [*facbase(n//i, i=i+1), n%i]
def is_non_inc(n): return (fb:=facbase(n)) == sorted(fb, reverse=True)
def a(n): return next(k for k in count(1) if is_non_inc(k*n))
print([a(n) for n in range(87)]) # Michael S. Branicky, Mar 09 2025

a(n) <= (n-1)! for any n > 0.

a(n) = 1 iff n belongs to A351987.

cp's OEIS Frontend

A223474 Least positive multiple of n that when written in base 10 has digits in nonincreasing order.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Perl