A348565 Numbers with factorial base expansion (d(1), ..., d(k)) such that, for i = 1..k, either d(i) > 0 and d(d(i)) = i or d(i) = 0.

0, 1, 2, 5, 6, 10, 14, 19, 23, 24, 36, 46, 54, 74, 86, 97, 109, 119, 120, 138, 168, 186, 204, 220, 238, 264, 282, 366, 414, 466, 482, 500, 530, 548, 566, 601, 619, 649, 667, 685, 701, 719, 720, 792, 834, 960, 1032, 1074, 1128, 1212, 1284, 1324, 1396, 1438

Offset

1,3

Comments

Leading zeros are ignored.

This sequence is a variant of A348056.

This sequence is infinite as it contains A000142 and A033312.

If m is a term, then so is A153880(m).

Links

Table of n, a(n) for n=1..54.

Index entries for sequences related to factorial base representation

Example

The first terms, alongside their factorial base expansion, are:
  n   a(n)  fact(a(n))
  --  ----  ----------
   1     0           0
   2     1           1
   3     2          10
   4     5          21
   5     6         100
   6    10         120
   7    14         210
   8    19         301
   9    23         321
  10    24        1000
  11    36        1200
  12    46        1320
  13    54        2100
  14    74        3010

Prog

(PARI) is(n) = { my (d=[]); for (r=2, oo, if (n==0, for (i=1, #d, if (d[i] && d[d[i]]!=i, return (0))); return (1), d=concat(n%r, d); n\=r)) }

Crossrefs

Cf. A000142, A033312, A048768, A153880, A348056.

Sequence in context: A102212 A191124 A281379 * A316946 A005984 A172186

Adjacent sequences: A348562 A348563 A348564 * A348566 A348567 A348568

Keyword

nonn,base

Author

Rémy Sigrist, Oct 22 2021

Status

approved