A134947 -id:A134947 - cp's OEIS frontend

A134698 Self-power numbers (or SPN's): numbers n with property that for each single digit d of n, we can also see the decimal expansion of the d-th power of some number as a substring of n and also n contains no 0's or 1's.

32564, 232564, 256432, 322564, 325642, 325643, 325644, 325645, 325646, 325648, 325664, 332564, 432564, 532564, 632564, 643256, 832564, 2232564, 2256432, 2322564, 2325642, 2325643, 2325644, 2325645, 2325646, 2325648, 2325664, 2332564, 2432564, 2532564

Offset: 1

Eric Angelini, Jul 05 2005

Computed by M. F. Hasler, Feb 02 2008, Feb 03 2008

There are an infinite number of SPN's, since for example we can prefix n by any digit of n.

			n = 32564 is a member because we can see a cube (64) in n, a square (4 or 25), a fifth power (32), a sixth power (64) and a fourth power (256).

M. F. Hasler, Table of n, a(n) for n = 1..1158

Cf. A134949, A134947, A134439, A134692, A134948.

More terms from M. F. Hasler, Feb 02 2008

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.

Original entry on oeis.org

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

Alexander R. Povolotsky, Feb 02 2008

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

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

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

Cf. A134698, A134947, A134439, A134692.

Cf. A000142.

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

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

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

A134949 Primitive self-power numbers (or SPN's): terms in A134698 which cannot be obtained by taking an earlier term M (say) of A134698 and prefixing, inserting or suffixing a digit of M.

Original entry on oeis.org

32564, 256432, 325648, 643256, 832564

Offset: 1

M. F. Hasler, Feb 02 2008

			232564 is an SPN but is not primitive since it can be obtained from the SPN 32564 by prefixing the digit 2.

Cf. A134698, A134947.

cp's OEIS Frontend

A134698 Self-power numbers (or SPN's): numbers n with property that for each single digit d of n, we can also see the decimal expansion of the d-th power of some number as a substring of n and also n contains no 0's or 1's.

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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.

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A134949 Primitive self-power numbers (or SPN's): terms in A134698 which cannot be obtained by taking an earlier term M (say) of A134698 and prefixing, inserting or suffixing a digit of M.

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