Kaprekar Series for the HP-41
Overview
-Take for example a 3-digit number, say N0 = 286
-Sort the digits in increasing order: 268 and
in decreasing order: 862
-Calculate the difference 862 - 268 = 594 = N1
-Repeat this operation: 954 - 459 = 495 = N2
-Again: 954 - 459 = 495 = N3
-The Kaprekar series in this example is 286 , 594 , 495 , 495
, .....
-So we end up in a 1-number cycle: { 495 }
-The following programs allows to find such cycles.
Program Listing
Data Registers: • R00 = n = number of digits ( 1 <= n <= 10 ) ( Register R00 is to be initialized before executing "KAPR" )
R01 thru R10 = digits of the numbers R11 & R12: temp
- R13 R14 R15 ..................... =
N0 N1 N2 .............................
Flags: /
Subroutine: "SORT" ( cf "Sorting
Numbers for the HP-41" )
-Line 27 may be replaced by an M-code routine SORT
-If you don't have an HP-41CX,
replace line 56 by RCL 11, line 52 by DSE
11, line 50 by CLX RCL IND 11 X=Y? , line
48 by STO 11, line 08 by RCL Z and delete line 05
| 01 LBL "KAPR"
02 VIEW X 03 12.012 04 STO 12 05 X<>Y 06 LBL 01 07 RCL 00 08 X<>Y 09 ISG 12 10 CLX 11 STO IND 12 12 LBL 02 13 RCL X |
14 10
15 MOD 16 STO IND Z 17 - 18 10 19 / 20 DSE Y 21 GTO 02 22 RCL 00 23 STO 11 24 E3 25 / 26 ISG X |
27 XEQ "SORT"
28 SIGN 29 0 30 ENTER^ 31 LBL 03 32 10 33 ST* Z 34 * 35 RCL IND Z 36 + 37 X<>Y 38 RCL IND 11 39 + |
40 X<>Y
41 ISG Z 42 CLX 43 DSE 11 44 GTO 03 45 - 46 VIEW X 47 RCL 12 48 X<>Y 49 LBL 04 50 X=NN? 51 GTO 05 52 DSE Y |
53 GTO 04
54 GTO 01 55 LBL 05 56 X<>Y 57 INT 58 RCL 12 59 INT 60 E3 61 / 62 + 63 CLD 64 END |
( 108 bytes / SIZE ? )
| STACK | INPUT | OUTPUT |
| X | N0 | bbb.eee |
where bbb.eee is the control number of the cycle
Example1: n = 6 & N0 = 918682
6 STO 00
918682 XEQ "KAPR" >>>> the HP-41 displays N0
, N1 , N2 , ...... and finally returns
24.030 ( in 4mn02s )
-So we eventually end up in a 7-number cycle in registers R24 , ..... , R30 namely:
{ 851742 , 750843 , 840852 , 860832
, 862632 , 642654 , 420876 }
Example2: n = 5 & N0 = 4 which will be read "00004" since n = 5
5 STO 00
4 R/S
>>>> 15.018 ( in 61 seconds )
-The 4-number cycle is in registers R15 thru R18:
{ 62964 , 71973 , 83952 , 74943
}