A067109 Number of occurrences of the string n in n! (A000142).

1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 1, 0, 2, 1, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 2, 4, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 2, 1, 2, 5, 0

Offset: 1

Author

Amarnath Murthy, Jan 08 2002

Keywords

• nonn
• base

Comments

a(A033180(n)) > 0. - Reinhard Zumkeller, Aug 23 2008

Examples

			a(4) = 1 as 4! = 24 and 4 occurs once;
a(5) = 0 as 5! = 120 does not contain a 5;
a(20) = 1 as 20! = 2432902008176640000 and 20 occurs once.
		

Links

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

Crossrefs

Cf. A000142, A033180.

Programs

Haskell

import Data.List (tails, isPrefixOf)
a067109 n = sum $
   map (fromEnum . (show n `isPrefixOf`)) (tails $ show $ a000142 n)
-- Reinhard Zumkeller, Aug 28 2014

Mathematica

Table[ Length[ StringPosition[ ToString[n! ], ToString[n]]], {n, 1, 75} ]
Table[SequenceCount[IntegerDigits[n!],IntegerDigits[n],Overlaps->True],{n,100}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 01 2019 *)

Extensions

More terms from Robert G. Wilson v, Jan 09 2002