A033180 Numbers k such that k! contains k as a string of digits.

1, 2, 4, 20, 21, 26, 30, 33, 37, 39, 42, 44, 45, 48, 51, 52, 53, 56, 59, 60, 64, 65, 67, 68, 69, 72, 75, 78, 79, 80, 81, 82, 83, 84, 88, 91, 93, 94, 95, 96, 97, 98, 99, 116, 124, 134, 136, 140, 141, 149, 164, 165, 166, 170, 174, 180, 186, 188, 196, 198, 200, 202, 205

Offset: 1

Author

Jeff Burch

Keywords

• nonn
• base
• easy
• nice

Links

• Mia Boudreau, Table of n, a(n) for n = 1..10000 (First 1000 terms from T. D. Noe)
• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A000142, A067109.

Programs

Haskell

a033180 n = a033180_list !! (n-1)
a033180_list = filter ((> 0) . a067109) [1..]
-- Reinhard Zumkeller, Aug 28 2014

Mathematica

Select[Range[210],MemberQ[Partition[IntegerDigits[#!],IntegerLength[#], 1], IntegerDigits[ #]]&] (* Harvey P. Dale, Dec 25 2011 *)
Select[Range@500, StringContainsQ[ToString[#!], ToString[#]] &] (* Ivan N. Ianakiev, Jul 28 2016 *)
Select[Range[210],SequenceCount[IntegerDigits[#!],IntegerDigits[#]]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 14 2017 *)

Python

from math import factorial
def ok(n): return str(n) in str(factorial(n))
print(list(filter(ok, range(206)))) # Michael S. Branicky, Aug 07 2021

Formula

A067109(a(n)) > 0. - Reinhard Zumkeller, Aug 23 2008

Extensions

More terms from David W. Wilson