login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A065794 Numbers n such that the sum of all possible subsets of the digits in n, excluding n itself, sums to n. 1
257982, 258564, 259146, 265707, 266193, 272754, 273336, 280383, 2176722, 2181960, 2309670, 2315448, 2320686, 4642524, 20096887, 20096935, 20097375, 20097423, 20206495, 20206543, 20207031, 40365992, 40366480, 40424038, 41102597, 41102645, 41103085 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The b-file lists all the terms in this finite sequence.

LINKS

Vadim Sheviakov, list of all 52 terms

EXAMPLE

a(1) = 257982 because the sum of all proper subsets of 257982 equals 2 + 8 + 82 + 9 + 92 + 98 + 982 + 7 + 72 + 78 + 782 + 79 + 792 + 798 + 7982 + 5 + 52 + 58 + 582 + 59 + 592 + 598 + 5982 + 57 + 572 + 578 + 5782 + 579 + 5792 + 5798 + 57982 + 2 + 22 + 28 + 282 + 29 + 292 + 298 + 2982 + 27 + 272 + 278 + 2782 + 279 + 2792 + 2798 + 27982 + 25 + 252 + 258 + 2582 + 259 + 2592 + 2598 + 25982 + 257 + 2572 + 2578 + 25782 + 2579 + 25792 + 25798 = 257982

MATHEMATICA

okQ[n_] := Module[{d=IntegerDigits[n]}, Total[FromDigits /@ Subsets[d]] == 2 n]; Reap[Do[If[okQ[n], Sow[n]], {n, 300000}]][[2, 1]]

PROG

(PARI) /* finds 8 digit terms */ for(n=10^7, 10^8-1, d8=Str(n-n\10*10); d7=Str((n-n\100*100)\10); d6=Str((n-n\1000*1000)\100); d5=Str((n-n\10^4*10^4)\1000); d4=Str((n-n\10^5*10^5)\10^4); d3=Str((n-n\10^6*10^6)\10^5); d2=Str((n-n\10^7*10^7)\10^6); d1=Str((n-n\10^8*10^8)\10^7); s=0-n; for(i1=0, 1, for(i2=0, 1, for(i3=0, 1, for(i4=0, 1, for(i5=0, 1, for(i6=0, 1, for(i7=0, 1, for(i8=0, 1, c=""; if(i1, c=concat(c, d1)); if(i2, c=concat(c, d2)); if(i3, c=concat(c, d3)); if(i4, c=concat(c, d4)); if(i5, c=concat(c, d5)); if(i6, c=concat(c, d6)); if(i7, c=concat(c, d7)); if(i8, c=concat(c, d8)); s=s+eval(c))))))))); if(n==s, print(n))) - Donovan Johnson

(Delphi) procedure TForm1.Button1Click(Sender: TObject);

var

  i, j, jj, k, l, n, m, t:longint;

  s:string;

  a:array of longint;

begin

  n:=UpDown1.Position;

  SetLength(a, n);

  for i:=0 to n-1 do a[i]:=0;

  t:=1;

  for i:=0 to n-1 do begin

    for j:=1 to trunc(power(2, n))-2 do begin

      s:=IntToStr(t+trunc(power(10, n))); delete(s, 1, 1); l:=0; jj:=j;

      for k:=1 to n do begin

        if jj mod 2 = 1 then begin

            delete(s, k-l, 1);

            l:=l+1;

        end;

        jj:=jj div 2;

      end;

      a[i]:=a[i]+StrToInt(s);

    end;

    t:=10*t;

  end;

  for i:=t div 10 to t-1 do begin

    m:=i; k:=0;

    for j:=0 to n-1 do begin

      k:=k+(m mod 10)*a[j];

      m:=m div 10;

    end;

    if i=k then Edit1.Text:=Edit1.Text+IntToStr(k)+'  ';

  end;

end; {Vadim Sheviakov}

CROSSREFS

Sequence in context: A105657 A251883 A251165 * A206253 A157670 A252921

Adjacent sequences:  A065791 A065792 A065793 * A065795 A065796 A065797

KEYWORD

base,nonn,fini,full

AUTHOR

Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Nov 19 2001

EXTENSIONS

a(15)-a(28) from Donovan Johnson, Jan 19 2011

a(29)-a(52) from Vadim Sheviakov, Jul 05 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 14 12:04 EST 2019. Contains 329979 sequences. (Running on oeis4.)