A321682 Numbers with distinct digits in factorial base.

0, 1, 2, 4, 5, 10, 13, 14, 19, 20, 22, 23, 46, 67, 68, 77, 82, 85, 86, 101, 106, 109, 110, 115, 116, 118, 119, 238, 355, 356, 461, 466, 469, 470, 503, 526, 547, 548, 557, 562, 565, 566, 623, 646, 667, 668, 677, 682, 685, 686, 701, 706, 709, 710, 715, 716, 718

Offset

1,3

Comments

This sequence is a variant of A010784; however here we have infinitely many terms (for example all the terms of A033312 belong to this sequence).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..8179 (terms up to 13!)

Index entries for sequences related to factorial base representation.

Example

The first terms, alongside the corresponding factorial base representations, are:
  n   a(n)  fac(a(n))
  --  ----  ---------
   1     0        (0)
   2     1        (1)
   3     2      (1,0)
   4     4      (2,0)
   5     5      (2,1)
   6    10    (1,2,0)
   7    13    (2,0,1)
   8    14    (2,1,0)
   9    19    (3,0,1)
  10    20    (3,1,0)
  11    22    (3,2,0)
  12    23    (3,2,1)
  13    46  (1,3,2,0)
  14    67  (2,3,0,1)

Maple

b:= proc(n, i) local r; `if`(n<i, [n],
      [b(iquo(n, i, 'r'), i+1)[], r])
    end:
t:= n-> (l-> is(nops(l)=nops({l[]})))(b(n, 2)):
select(t, [$0..1000])[];  # Alois P. Heinz, Nov 16 2018

Mathematica

q[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; UnsameQ @@ s]; Select[Range[0, 720], q] (* Amiram Eldar, Feb 21 2024 *)

Prog

(PARI) is(n) = my (s=0); for (k=2, oo, if (n==0, return (1)); my (d=n%k); if (bittest(s, d), return (0), s+=2^d; n\=k))

Crossrefs

Cf. A010784, A033312, A108731.

Sequence in context: A325676 A097132 A321683 * A013578 A283204 A105138

Adjacent sequences: A321679 A321680 A321681 * A321683 A321684 A321685

Keyword

nonn,base

Author

Rémy Sigrist, Nov 16 2018

Status

approved