# Self Power Numbers - Unfinished business!

Alexander Povolotsky apovolot at gmail.com
Sat Feb 2 19:23:47 CET 2008

```Will one end this at single digit (power = 9) or alternatively instead seek
multi-consecutive-digit power presentations: such as power of  10, etc. ?

On Feb 2, 2008 1:05 PM, Maximilian Hasler <maximilian.hasler at gmail.com>
wrote:

> On Feb 2, 2008 7:01 PM, N. J. A. Sloane <njas at research.att.com> wrote:
> > The number N=325648 might be called a self-power number because:
> > "3" means "a cube is visible in N"     (yes, it is "8" -- 8=2*2*2)
> > "2" means "a square is visible in N"    (yes, it is "25" -- 25=5*5)
> > "5" means "a power 5 is visible in N"     (yes, it is "32" = 2*2*2*2*2)
> > "6" means "a power 6 is visible in N"     (yes, it is "64" =
> 2*2*2*2*2*2)
> > "4" means "a power 4 is visible in N"     (yes, it is "256" = 4*4*4*4*)
> > "8" means "a power 8 is visible in N"     (yes, it is "256"
> =2*2*2*2*2*2*2*2)
> > ["visible" means "as a whole": "25" is NOT visible in 235]
> > Can someone compute all such SPN _which don't include any 0's or 1's_ ?
> > Feb 02 2008:  Would someone kindly work out the first few SPN's
> > and send them to me? Better use email, the OEIS machine is down.
>
> the unoptimized PARI code I include below gives:
>
> 32564,232564,256432,322564,325642,325643,325644,325645,325646,325648,325664,
> 332564,432564,532564,632564,643256,832564,
>
> Regards,
> Maximilian
>
> isSPN(n)={ local( V=Vec(Str(n)), S=eval(Set(V)), t); S[1]<2 & return;
> /* disallow 0 ot 1*/
>  t=eval( Set( concat( vector( #V,a,vector( a,b,concat( vecextract(
> V,2^a-2^(b-1))))))));
>  for(i=1,#S, for(j=1,#t, floor(sqrtn(t[j]+.5,S[i]))^S[i]==t[j] &
> next(2) /*OK: goto next power*/);
>  return /*not OK*/); n}
>
> for(n=1,10^9, isSPN(n) |next; print1(n","))
>
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