A   Narcissistic decimal number   is a non-negative integer,   



n


{\displaystyle n}

,   that is equal to the sum of the   



m


{\displaystyle m}

-th   powers of each of the digits in the decimal representation of   



n


{\displaystyle n}

,   where   



m


{\displaystyle m}

   is the number of digits in the decimal representation of   



n


{\displaystyle n}

.



Narcissistic (decimal) numbers are sometimes called   Armstrong   numbers, named after Michael F. Armstrong.

They are also known as   Plus Perfect   numbers.



An example

   if   



n


{\displaystyle n}

   is   153 
   then   



m


{\displaystyle m}

,   (the number of decimal digits)   is   3 
   we have    13 + 53 + 33   =   1 + 125 + 27   =   153  
   and so   153   is a narcissistic decimal number


Task

Generate and show here the first   25   narcissistic decimal numbers.



Note:   




0

1


=
0


{\displaystyle 0^{1}=0}

,   the first in the series.



See also

   the  OEIS entry:     Armstrong (or Plus Perfect, or narcissistic) numbers.
   MathWorld entry:   Narcissistic Number.
   Wikipedia entry:     Narcissistic number.


 1 DIM K(10): DIM M(10)
 2 FOR Y=0 TO 9: LET M(Y+1)=Y: NEXT Y
 3 FOR N=1 TO 7
 4 FOR J=N TO 0 STEP -1
 5 FOR I=N-J TO 0 STEP -1
 6 FOR H=N-J-I TO 0 STEP -1
 7 FOR G=N-J-I-H TO 0 STEP -1
 8 FOR F=N-J-I-H-G TO 0 STEP -1
 9 FOR E=N-J-I-H-G-F TO 0 STEP -1
10 FOR D=N-J-I-H-G-F-E TO 0 STEP -1
11 FOR C=N-J-I-H-G-F-E-D TO 0 STEP -1
12 FOR B=N-J-I-H-G-F-E-D-C TO 0 STEP -1
13 LET A=N-J-I-H-G-F-E-D-C-B
14 LET X=B+C*M(3)+D*M(4)+E*M(5)+F*M(6)+G*M(7)+H*M(8)+I*M(9)+J*M(10)
15 LET S$=STR$ (X)
16 IF LEN (S$)<N THEN GO TO 34
17 IF LEN (S$)<>N THEN GO TO 33
18 FOR Y=1 TO 10: LET K(Y)=0: NEXT Y
19 FOR Y=1 TO N
20 LET Z= CODE (S$(Y))-47
21 LET K(Z)=K(Z)+1
22 NEXT Y
23 IF A<>K(1) THEN GO TO 33
24 IF B<>K(2) THEN GO TO 33
25 IF C<>K(3) THEN GO TO 33
26 IF D<>K(4) THEN GO TO 33
27 IF E<>K(5) THEN GO TO 33
28 IF F<>K(6) THEN GO TO 33
29 IF G<>K(7) THEN GO TO 33
30 IF H<>K(8) THEN GO TO 33
31 IF I<>K(9) THEN GO TO 33
32 IF J=K(10) THEN PRINT X,
33 NEXT B: NEXT C: NEXT D: NEXT E: NEXT F: NEXT G: NEXT H: NEXT I: NEXT J
34 FOR Y=2 TO 9
35 LET M(Y+1)=M(Y+1)*Y
36 NEXT Y
37 NEXT N
38 PRINT
39 PRINT "DONE"