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

Author

Reinhard Zumkeller, Apr 10 2004

Keywords

• nonn
• base

Comments

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

Examples

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

Crossrefs

Cf. A036603, A007088, A000142, A093826.

Programs

Mathematica

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

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

Extensions

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