A373084 Numbers k such that the sums of digits of k and 1/k in factorial base (A007623) are equal.

1, 2, 3, 6, 12, 15, 24, 45, 70, 105, 120, 576, 700, 720, 1008, 1152, 4800, 5040, 5670, 8960, 14175, 17820, 18711, 24640, 25920, 28800, 32256, 33264, 36960, 39312, 39936, 40320, 64800, 69498, 88452, 89600, 90720, 98560, 118272, 120960, 138996, 147840, 164736, 193536

Offset

1,2

Comments

Numbers k such that A034968(k) = A276350(k).

All the factorials (A000142) are terms, since A034968(k!) = A276350(k!) = 1 for k >= 0.

Links

Table of n, a(n) for n=1..44.

Wikipedia, Factorial number system.

Index entries for sequences related to factorial base representation.

Example

The first 6 terms are:
  n  a(n)   a(n) in factorial base  1/a(n) in factorial base  sum of digits
  -  ----   ----------------------  ------------------------  -------------
  1     1                       1   1                         1
  2     2                      10   0.01                      1
  3     3                      11   0.002                     2
  4     6                     100   0.001                     1
  5    12                     200   0.0002                    2
  6    15                     211   0.00013                   4

Mathematica

Select[Range[1000], Total@ NumberDecompose[#, Reverse@Range[#]!] == Total@ NumberDecompose[1/#, 1/Range[#]!] &]

Crossrefs

Cf. A000142, A007623, A034968, A276350.

Sequence in context: A070926 A226023 A124485 * A200175 A286906 A125867

Adjacent sequences: A373081 A373082 A373083 * A373085 A373086 A373087

Keyword

nonn,base

Author

Amiram Eldar, May 23 2024

Status

approved