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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. 3

%I

%S 1,2,10,11,12,21,22,24,100,101,102,110,111,112,120,121,122,124,201,

%T 210,211,212,221,222,224,241,242,244,424,1000,1001,1002,1010,1011,

%U 1012,1020,1021,1022,1024,1100,1101,1102,1110,1111,1112,1120,1121,1122,1124,1200

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

%p 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 For C++ program see the Applegate link in A135463.

%o (Haskell)

%o import Data.List (nub, sort, isInfixOf)

%o a134948 n = a134948_list !! (n-1)

%o a134948_list = filter h [0..] where

%o h x = all (`isInfixOf` xs)

%o (map (fss !!) $ map (read . return) $ sort $ nub xs)

%o where xs = show x

%o fss = map show $ take 10 a000142_list

%o -- _Reinhard Zumkeller_, Sep 26 2014

%Y Cf. A134698, A134947, A134439, A134692.

%Y Cf. A000142.

%K nonn,base

%O 1,2

%A _Alexander R. Povolotsky_, Feb 02 2008

%E a(1) - a(18) computed by _N. J. A. Sloane_, Feb 02 2008

%E a(19) onwards from _David Applegate_, Feb 09 2008

%E More terms from _R. J. Mathar_, Feb 05 2008

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Last modified July 15 20:24 EDT 2019. Contains 325056 sequences. (Running on oeis4.)