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

1,2

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Index entries for sequences related to factorial numbers

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A000142.

Sequence in context: A133521 A122158 A178223 * A215815 A295826 A201502

Adjacent sequences: A033177 A033178 A033179 * A033181 A033182 A033183

Keyword

nonn,base,easy,nice

Author

Jeff Burch

Extensions

More terms from David W. Wilson

Status

approved