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

1,2

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

Links

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

Example

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

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

Prog

For C++ program see the Applegate link in A135463.
(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

Crossrefs

Cf. A134698, A134947, A134439, A134692.

Cf. A000142.

Sequence in context: A136816 A188264 A169683 * A060045 A340051 A000462

Adjacent sequences: A134945 A134946 A134947 * A134949 A134950 A134951

Keyword

nonn,base

Author

Alexander R. Povolotsky, Feb 02 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

Status

approved