A093685 In binary representation: numbers not occurring in their factorial.

0, 5, 11, 13, 15, 17, 31, 37, 55, 81, 164, 395, 513, 517, 619, 1041, 1287, 1538, 2108, 2116, 2137, 2138, 2282, 2352, 2363, 2432, 2466, 2524, 4278, 4511, 4758, 4766, 4852, 4854, 5136, 5586, 8396, 8463, 8883, 9707, 10351, 16528, 17279, 19469, 21244, 24472

Offset

1,2

Comments

A093684(a(n)) = 0, complement of A093686.

Links

Table of n, a(n) for n=1..46.

Example

5! = 1*2*3*4*5 = 120 -> '1111000', in which '101'=5 is not contained, so 5 is in the sequence.

Mathematica

f[n_] := ToString[ FromDigits[ IntegerDigits[n, 2]]]; Select[ Range[ 29000], StringPosition[ f[ #! ], f[ # ]] == {} &] (* Robert G. Wilson v, Apr 15 2004 *)

Prog

(Python)
def aupto(limit):
  kfact, alst = 1, [0]
  for k in range(1, limit+1):
    kb, kfact = bin(k)[2:], kfact * k
    kfactb = bin(kfact)[2:]
    if kb not in kfactb: alst.append(k)
  return alst
print(aupto(25000)) # Michael S. Branicky, May 01 2021

Crossrefs

Cf. A036603, A007088, A000142, A093826.

Sequence in context: A287123 A227146 A251965 * A337658 A206548 A206547

Adjacent sequences: A093682 A093683 A093684 * A093686 A093687 A093688

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 10 2004

Extensions

More terms from Robert G. Wilson v, Apr 15 2004

Status

approved