A134948 Self-factorial numbers: numbers n with property that for each single digit d of n, we can also see the decimal expansion of d! as a substring of n.

1, 2, 10, 11, 12, 21, 22, 24, 100, 101, 102, 110, 111, 112, 120, 121, 122, 124, 201, 210, 211, 212, 221, 222, 224, 241, 242, 244, 424, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1022, 1024, 1100, 1101, 1102, 1110, 1111, 1112, 1120, 1121, 1122, 1124, 1200

Offset: 1

Author

Alexander R. Povolotsky, Feb 02 2008

Keywords

• nonn
• base

Comments

As 9 does not occur in d! for all d in {0..9}, all self-factorials cannot contain 9 as a digit, cf. A007095. - Reinhard Zumkeller, Sep 26 2014

Examples

			24 is a self-factorial number because we can see both 2! = 2 and 4! = 24 in the decimal expansion 24.
		

Links

• D. Applegate and R. Zumkeller, Table of n, a(n) for n = 1..10000 (first 300 terms from David Applegate)

Crossrefs

Cf. A134698, A134947, A134439, A134692.

Cf. A000142.

Programs

Haskell

import Data.List (nub, sort, isInfixOf)
a134948 n = a134948_list !! (n-1)
a134948_list = filter h [0..] where
   h x = all (`isInfixOf` xs)
             (map (fss !!) $ map (read . return) $ sort $ nub xs)
         where xs = show x
   fss = map show $ take 10 a000142_list
-- Reinhard Zumkeller, Sep 26 2014

Maple

isA134948 := proc(n) local nbase10,dgs,d,dfac ; nbase10 := convert(n,base,10) ; dgs := convert(nbase10,set) ; for d in dgs do dfac := convert(d!,base,10) ; if verify(dfac,nbase10,'sublist') = false then RETURN(false) ; fi ; od: RETURN(true) ; end: for n from 1 to 10000 do if isA134948(n) then printf("%d ",n) ; fi ; od: # R. J. Mathar, Feb 05 2008

Extensions

a(1) - a(18) computed by N. J. A. Sloane, Feb 02 2008

a(19) onwards from David Applegate, Feb 09 2008

More terms from R. J. Mathar, Feb 05 2008