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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
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 (list; graph; refs; listen; history; text; internal format)
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 A000462 A282093

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

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Last modified June 25 12:55 EDT 2019. Contains 324352 sequences. (Running on oeis4.)