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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.

%I A134948 #17 Jan 16 2018 02:46:03
%S A134948 1,2,10,11,12,21,22,24,100,101,102,110,111,112,120,121,122,124,201,
%T A134948 210,211,212,221,222,224,241,242,244,424,1000,1001,1002,1010,1011,
%U A134948 1012,1020,1021,1022,1024,1100,1101,1102,1110,1111,1112,1120,1121,1122,1124,1200
%N 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.
%C A134948 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
%H A134948 D. Applegate and R. Zumkeller, <a href="/A134948/b134948.txt">Table of n, a(n) for n = 1..10000</a> (first 300 terms from David Applegate)
%e A134948 24 is a self-factorial number because we can see both 2! = 2 and 4! = 24 in the decimal expansion 24.
%p A134948 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
%o A134948 For C++ program see the Applegate link in A135463.
%o A134948 (Haskell)
%o A134948 import Data.List (nub, sort, isInfixOf)
%o A134948 a134948 n = a134948_list !! (n-1)
%o A134948 a134948_list = filter h [0..] where
%o A134948    h x = all (`isInfixOf` xs)
%o A134948              (map (fss !!) $ map (read . return) $ sort $ nub xs)
%o A134948          where xs = show x
%o A134948    fss = map show $ take 10 a000142_list
%o A134948 -- _Reinhard Zumkeller_, Sep 26 2014
%Y A134948 Cf. A134698, A134947, A134439, A134692.
%Y A134948 Cf. A000142.
%K A134948 nonn,base
%O A134948 1,2
%A A134948 _Alexander R. Povolotsky_, Feb 02 2008
%E A134948 a(1) - a(18) computed by _N. J. A. Sloane_, Feb 02 2008
%E A134948 a(19) onwards from _David Applegate_, Feb 09 2008
%E A134948 More terms from _R. J. Mathar_, Feb 05 2008