PALINDROME FORMATION TESTED TO A MAXIMUM OF 100 DIGITS
OCT. 24 1979
DATA FOR 3-DIGIT DECIMAL NUMBERS
WHICH CAN BE GROUPED INTO 180 CLASSES
INTRANSIGENT CLASSES DEFINED BY REVERSED DIGIT ADDITIONS, WITHOUT CARRIES
SUM1 MID# SUM1 MID# SUM1 MID#
7 9 15 8 17 7
23 MAX ADDS FOR 177 PALINDROME CLASSES, WITH 3 INTRANSIGENT CLASSES
PALINDROMES GROUPED AS TO THEIR ADD DEPTHS
ADDS CLASSES ADDS CLASSES ADDS CLASSES ADDS CLASSES
0 20 1 41 2 53 3 23
4 18 5 5 6 4 7 3
8 2 10 1 11 1 14 1
15 1 17 2 22 1 23 1
DATA FOR 4-DIGIT DECIMAL NUMBERS
WHICH CAN BE GROUPED INTO 342 CLASSES
INTRANSIGENT CLASSES DEFINED BY REVERSED DIGIT ADDITIONS, WITHOUT CARRIES
* MEANS,- ONE NUMBER IN THIS CLASS IS AN INITIAL PALINDROME
SUM1 SUM2 SUM1 SUM2 SUM1 SUM2
6 13 8 13 8 18 *
13 7 13 16 16 5
16 14 * 17 7 17 8
17 16 17 17
21 MAX ADDS FOR 331 PALINDROME CLASSES, WITH 11 INTRANSIGENT CLASSES
PALINDROMES GROUPED AS TO THEIR ADD DEPTHS
0-ADD GROUP ALSO INCLUDES INDIVIDUAL PALINDROMES INDICATED BY * ABOVE
ADDS CLASSES ADDS CLASSES ADDS CLASSES ADDS CLASSES
0 4 1 91 2 88 3 31
4 40 5 17 6 10 7 12
8 8 9 2 10 2 11 4
12 4 13 5 15 5 16 2
17 1 18 1 20 3 21 1
DATA FOR 5-DIGIT DECIMAL NUMBERS
WHICH CAN BE GROUPED INTO 3420 CLASSES
INTRANSIGENT CLASSES DEFINED BY REVERSED DIGIT ADDITIONS, WITHOUT CARRIES
* MEANS,- ONE NUMBER IN THIS CLASS IS AN INITIAL PALINDROME
SUM1 SUM2 MID# SUM1 SUM2 MID# SUM1 SUM2 MID#
1 16 1 2 2 8 * 3 12 3
3 16 2 3 18 7 4 3 9
4 4 8 * 4 5 5 4 5 6
4 6 5 * 4 6 6 * 4 6 9 *
4 8 5 * 4 8 7 * 4 8 8 *
4 8 9 * 4 11 3 4 11 7
4 12 3 * 4 14 3 * 4 18 7 *
4 18 8 * 5 12 6 5 17 1
6 1 7 6 3 7 6 6 9 *
6 8 5 * 6 8 7 * 6 8 9 *
6 13 9 6 18 4 * 7 4 7
7 12 5 7 13 0 7 17 0
7 17 5 8 7 5 8 7 8
8 7 9 8 8 7 * 8 9 6
8 11 0 8 11 2 8 11 7
8 12 0 * 8 12 1 * 8 12 3 *
8 12 5 * 8 12 9 * 8 13 0
8 13 1 8 13 2 8 13 3
8 13 8 8 14 2 * 8 14 5 *
8 15 5 8 15 7 8 16 2 *
8 16 5 * 8 16 6 * 8 16 8 *
8 17 0 8 17 4 8 17 5
8 17 6 8 17 7 8 17 8
8 18 3 * 8 18 7 * 9 2 7
9 3 5 9 3 6 9 4 7
9 6 6 9 8 7 9 10 8
9 11 8 9 13 6 9 16 4
9 17 5 9 17 7 9 18 0
9 18 9 10 6 9 * 10 15 9
11 5 3 11 5 4 11 14 3
11 14 4 11 18 4 11 18 8
12 2 9 * 12 3 4 12 4 8 *
12 5 9 12 7 4 12 7 9
12 8 0 * 12 8 3 * 12 8 4 *
12 8 8 * 12 9 3 12 11 9
12 12 4 * 12 13 8 12 14 9 *
12 16 4 * 12 16 9 * 12 17 0
12 17 3 12 17 4 12 17 8
13 2 4 13 4 4 13 6 0
13 7 9 13 11 4 13 13 4
13 15 0 13 16 9 14 6 5 *
14 7 5 14 9 4 14 15 5
14 16 5 * 14 18 2 * 15 5 1
15 5 6 15 6 1 15 8 2
15 8 4 15 8 6 15 14 1
15 14 6 15 15 1 15 17 2
15 17 4 15 17 6 15 18 2
15 18 4 15 18 6 16 4 9 *
16 5 3 16 5 5 16 6 0 *
16 6 6 * 16 6 8 * 16 7 3
16 8 4 * 16 13 9 16 14 3 *
16 14 5 * 16 15 0 16 15 6
16 15 8 16 16 3 * 16 17 4
16 18 1 * 17 2 1 17 2 5
17 3 2 17 3 4 17 3 5
17 3 6 17 4 0 17 4 1
17 4 3 17 4 6 17 4 7
17 4 8 17 5 0 17 5 1
17 5 9 17 6 0 17 6 1
17 6 2 17 6 3 17 6 5
17 6 6 17 6 7 17 7 2
17 7 7 17 8 2 17 8 4
17 8 5 17 8 6 17 9 1
17 9 2 17 11 1 17 11 5
17 12 2 17 12 4 17 12 5
17 12 6 17 13 0 17 13 1
17 13 3 17 13 6 17 13 7
17 13 8 17 14 0 17 14 1
17 14 9 17 15 0 17 15 1
17 15 2 17 15 3 17 15 5
17 15 6 17 15 7 17 16 2
17 16 7 17 17 2 17 17 4
17 17 5 17 17 6 17 18 0
17 18 3 17 18 5 17 18 6
17 18 8 18 1 3 18 1 7
18 4 2 * 18 5 4 18 7 0
18 7 2 18 7 3 18 7 5
18 7 9 18 8 4 * 18 8 5 *
18 9 4 18 10 3 * 18 10 7 *
18 13 2 18 14 4 * 18 16 0 *
18 16 2 * 18 16 3 * 18 16 5 *
18 16 9 * 18 17 4 18 17 5
55 MAX ADDS FOR 3174 PALINDROME CLASSES, WITH 246 INTRANSIGENT CLASSES
PALINDROMES GROUPED AS TO THEIR ADD DEPTHS
0-ADD GROUP ALSO INCLUDES INDIVIDUAL PALINDROMES INDICATED BY * ABOVE
ADDS CLASSES ADDS CLASSES ADDS CLASSES ADDS CLASSES
0 40 1 447 2 752 3 448
4 407 5 211 6 180 7 108
8 101 9 75 10 72 11 61
12 49 13 36 14 26 15 24
16 14 17 11 18 13 19 9
20 13 21 7 22 3 23 6
24 8 25 5 26 4 27 4
28 5 29 7 30 5 31 3
32 1 33 2 37 2 38 5
39 2 40 1 47 2 52 2
53 1 54 1 55 1
DATA FOR 6-DIGIT DECIMAL NUMBERS
WHICH CAN BE GROUPED INTO 6498 CLASSES
INTRANSIGENT CLASSES DEFINED BY REVERSED DIGIT ADDITIONS, WITHOUT CARRIES
* MEANS,- ONE NUMBER IN THIS CLASS IS AN INITIAL PALINDROME
SUM1 SUM2 SUM3 SUM1 SUM2 SUM3 SUM1 SUM2 SUM3
1 1 18 1 3 15 1 3 16
1 5 18 1 7 15 1 8 17
1 8 18 1 13 5 1 13 17
1 13 18 1 14 7 1 15 7
1 15 13 1 15 16 1 15 17
1 16 16 1 17 14 1 18 2
1 18 4 1 18 5 1 18 9
1 18 12 2 2 16 * 2 2 17
2 2 18 * 2 3 17 2 5 18
2 7 11 2 7 13 2 11 16
2 11 17 2 15 8 2 15 10
2 15 11 2 17 6 2 17 10
2 17 15 2 17 17 2 17 18
2 18 6 * 3 2 16 3 4 16
3 5 11 3 5 13 3 6 11
3 7 11 3 7 16 3 7 18
3 8 14 3 8 15 3 8 18
3 10 15 3 10 16 3 11 8
3 11 14 3 11 15 3 11 16
3 13 14 3 15 10 3 16 5
3 16 9 3 16 11 3 16 12
3 17 0 3 17 6 3 17 17
3 18 5 3 18 12 3 18 16
3 18 18 4 1 18 4 2 18 *
4 4 15 4 5 13 4 5 15
4 5 17 4 5 18 4 6 10 *
4 6 12 * 4 6 13 4 6 18 *
4 7 15 4 8 12 * 4 8 14 *
4 8 17 4 10 6 * 4 10 18 *
4 11 16 4 11 17 4 12 6 *
4 12 18 * 4 13 6 4 14 5
4 14 7 4 14 16 * 4 15 3
4 15 7 4 16 13 4 16 18 *
4 17 6 4 18 3 4 18 5
4 18 6 * 4 18 8 * 4 18 9
4 18 17 5 0 14 5 1 13
5 3 14 5 3 16 5 4 18
5 7 17 5 10 16 5 10 17
5 10 18 5 11 2 5 11 4
5 11 7 5 12 4 5 12 8
5 12 18 5 14 4 5 14 13
5 15 2 5 15 3 5 15 12
5 15 16 5 15 18 5 16 13
5 16 18 5 18 18 6 0 12 *
6 0 13 6 2 14 * 6 5 13
6 6 18 * 6 8 14 * 6 8 16 *
6 8 17 6 9 13 6 10 2 *
6 10 17 6 11 3 6 11 7
6 11 8 6 11 18 6 12 2 *
6 12 4 * 6 12 8 * 6 13 3
6 13 6 6 13 18 6 14 1
6 14 5 6 14 6 * 6 14 11
6 14 12 * 6 14 16 * 6 15 3
6 15 12 6 15 13 6 15 17
6 16 13 6 16 16 * 6 16 18 *
6 17 9 6 17 11 6 17 17
6 18 10 * 6 18 11 6 18 15
7 1 12 7 1 14 7 2 17
7 3 10 7 3 12 7 3 14
7 3 17 7 5 13 7 7 10
7 7 15 7 7 17 7 8 12
7 10 18 7 11 2 7 11 13
7 12 6 7 12 11 7 13 0
7 13 1 7 13 4 7 13 6
7 13 9 7 13 13 7 14 0
7 14 1 7 14 13 7 15 16
7 16 8 7 16 11 7 17 6
7 17 11 7 17 14 7 17 15
7 17 18 7 18 4 7 18 8
7 18 14 7 18 15 8 0 13
8 0 17 8 1 10 8 1 14
8 1 16 8 2 12 * 8 2 13
8 3 12 8 3 16 8 3 17
8 4 13 8 4 17 8 5 17
8 6 16 * 8 6 18 * 8 7 12
8 7 14 8 9 11 8 9 12
8 10 3 8 10 4 * 8 11 4
8 11 6 8 11 7 8 11 11
8 11 14 8 11 15 8 11 17
8 12 2 * 8 12 4 * 8 12 6 *
8 12 7 8 12 9 8 12 10 *
8 12 11 8 12 14 * 8 12 18 *
8 13 1 8 13 2 8 13 5
8 13 7 8 13 14 8 13 17
8 14 2 * 8 14 3 8 14 5
8 14 6 * 8 14 7 8 14 8 *
8 14 9 8 14 10 * 8 14 11
8 14 12 * 8 14 17 8 14 18 *
8 15 11 8 15 12 8 15 18
8 16 0 * 8 16 1 8 16 3
8 16 6 * 8 16 9 8 16 11
8 16 12 * 8 16 16 * 8 16 18 *
8 17 0 8 17 4 8 17 5
8 17 6 8 17 9 8 17 10
8 17 12 8 17 15 8 17 16
8 18 0 * 8 18 3 8 18 9
8 18 10 * 8 18 11 8 18 12 *
8 18 13 8 18 16 * 8 18 17
9 0 12 9 0 13 9 0 18
9 1 11 9 1 15 9 1 18
9 3 14 9 3 15 9 3 16
9 4 10 9 4 13 9 5 13
9 5 18 9 6 10 9 6 13
9 6 14 9 6 16 9 7 17
9 8 11 9 8 15 9 8 18
9 9 14 9 10 6 9 10 7
9 10 15 9 10 16 9 13 8
9 13 17 9 13 18 9 14 4
9 14 13 9 16 2 9 16 4
9 16 7 9 16 8 9 16 11
9 16 13 9 16 16 9 16 17
9 17 0 9 17 7 9 17 9
9 17 16 9 18 18 10 0 8 *
10 0 17 10 1 9 10 1 18
10 3 7 10 3 16 10 6 6 *
10 6 15 10 7 4 10 7 9
10 7 13 10 7 18 10 8 9
10 8 18 * 10 9 17 10 10 18 *
10 12 7 10 12 16 * 10 15 6
10 15 15 10 16 4 * 10 16 13
10 16 18 * 10 17 18 10 18 6 *
10 18 15 10 18 18 * 11 1 5
11 1 7 11 1 9 11 1 14
11 1 16 11 1 18 11 2 5
11 2 6 11 2 9 11 2 14
11 2 15 11 2 18 11 4 8
11 4 9 11 4 17 11 4 18
11 5 9 11 5 18 11 8 9
11 8 18 11 9 8 11 10 5
11 10 7 11 10 14 11 10 16
11 10 18 11 11 5 11 11 6
11 11 14 11 11 15 11 11 18
11 13 8 11 13 17 11 13 18
11 14 18 11 17 18 11 18 3
11 18 4 11 18 6 11 18 12
11 18 13 11 18 15 12 0 7
12 0 16 * 12 1 5 12 1 7
12 1 14 12 1 16 12 2 7
12 2 9 12 2 16 * 12 2 18 *
12 4 8 * 12 4 17 12 5 9
12 5 18 12 6 9 12 6 18 *
12 8 0 * 12 8 4 * 12 8 6 *
12 8 13 12 8 15 12 9 4
12 9 16 12 10 5 12 10 7
12 10 14 * 12 10 16 * 12 11 7
12 11 16 12 11 18 12 13 8
12 13 17 12 14 18 * 12 15 18
12 17 0 12 17 4 12 17 6
12 17 9 12 17 13 12 17 15
12 18 4 * 12 18 13 12 18 18 *
13 0 5 13 0 14 13 1 7
13 1 16 13 2 6 13 2 7
13 2 8 13 2 15 13 2 16
13 2 17 13 3 9 13 3 18
13 4 5 13 4 8 13 4 9
13 4 14 13 4 17 13 4 18
13 6 0 13 6 4 13 6 7
13 6 13 13 6 16 13 7 9
13 7 18 13 8 2 13 8 3
13 8 4 13 8 11 13 8 12
13 8 13 13 9 4 13 9 6
13 9 7 13 9 14 13 10 7
13 10 16 13 11 6 13 11 7
13 11 8 13 11 15 13 11 16
13 11 17 13 12 18 13 13 5
13 13 8 13 13 14 13 13 17
13 13 18 13 15 0 13 15 4
13 15 7 13 15 9 13 15 13
13 15 16 13 16 18 13 17 2
13 17 3 13 17 4 13 17 11
13 17 12 13 17 13 13 18 2
13 18 3 13 18 4 13 18 11
13 18 12 13 18 13 13 18 18
14 2 7 14 2 16 * 14 3 5
14 3 9 14 3 14 14 3 18
14 5 6 14 5 15 14 6 1
14 6 2 * 14 6 6 * 14 6 10 *
14 6 11 14 6 15 14 7 1
14 7 5 14 7 6 14 7 9
14 7 10 14 7 14 14 7 15
14 7 18 14 8 5 14 8 14 *
14 9 2 14 9 8 14 11 7
14 11 16 14 12 5 14 12 14 *
14 12 18 * 14 14 6 * 14 14 15
14 15 1 14 15 2 14 15 6
14 15 10 14 15 11 14 15 15
14 16 1 14 16 5 14 16 6 *
14 16 10 * 14 16 14 * 14 16 15
14 16 18 * 14 17 5 14 17 14
14 18 8 * 14 18 17 15 1 9
15 1 18 15 2 5 15 2 14
15 3 8 15 3 17 15 4 4
15 4 13 15 5 4 15 5 13
15 6 1 15 6 3 15 6 4
15 6 9 15 6 10 15 6 12
15 6 13 15 6 18 15 7 0
15 7 8 15 7 17 15 8 1
15 8 3 15 8 10 15 8 12
15 9 8 15 10 18 15 11 5
15 11 14 15 12 8 15 12 17
15 13 4 15 13 13 15 14 4
15 14 13 15 15 1 15 15 3
15 15 4 15 15 10 15 15 12
15 15 13 15 15 18 15 16 0
15 16 8 15 16 9 15 16 17
15 17 1 15 17 3 15 17 10
15 17 12 15 18 3 15 18 12
16 0 5 16 0 6 * 16 0 9
16 0 14 * 16 0 15 16 0 18 *
16 1 6 16 1 7 16 1 15
16 1 16 16 2 6 * 16 2 9
16 2 15 16 2 18 * 16 3 1
16 3 4 16 3 9 16 3 10
16 3 13 16 3 18 16 4 4 *
16 4 8 * 16 4 9 16 4 13
16 4 17 16 4 18 * 16 5 5
16 5 7 16 5 14 16 5 16
16 6 0 * 16 6 5 16 6 14 *
16 7 4 16 7 5 16 7 6
16 7 13 16 7 14 16 7 15
16 9 6 16 9 7 16 9 8
16 9 14 16 9 15 16 9 18
16 10 6 * 16 10 7 16 10 15
16 10 16 * 16 11 6 16 11 15
16 11 18 16 12 1 16 12 4 *
16 12 10 * 16 12 13 16 12 18 *
16 13 4 16 13 8 16 13 13
16 13 17 16 13 18 16 14 5
16 14 7 16 14 14 * 16 14 16 *
16 15 0 16 15 5 16 15 9
16 15 14 16 16 4 * 16 16 5
16 16 6 * 16 16 13 16 16 14 *
16 16 15 16 18 1 16 18 4 *
16 18 6 * 16 18 10 * 16 18 13
16 18 15 17 0 7 17 0 9
17 0 16 17 0 18 17 2 4
17 2 6 17 2 9 17 2 13
17 2 15 17 2 18 17 3 1
17 3 3 17 3 4 17 3 7
17 3 10 17 3 12 17 3 13
17 3 16 17 4 0 17 4 4
17 4 5 17 4 6 17 4 9
17 4 13 17 4 14 17 4 15
17 4 18 17 5 0 17 5 1
17 5 2 17 5 4 17 5 9
17 5 10 17 5 11 17 5 13
17 5 18 17 6 0 17 6 2
17 6 3 17 6 5 17 6 6
17 6 11 17 6 12 17 6 14
17 6 15 17 7 1 17 7 7
17 7 10 17 7 16 17 8 0
17 8 2 17 8 4 17 8 5
17 8 6 17 8 7 17 8 8
17 8 11 17 8 13 17 8 14
17 8 15 17 8 16 17 8 17
17 9 0 17 9 2 17 9 3
17 9 4 17 9 5 17 9 6
17 9 16 17 9 18 17 11 4
17 11 6 17 11 13 17 11 15
17 11 18 17 12 1 17 12 3
17 12 4 17 12 7 17 12 10
17 12 12 17 12 13 17 12 16
17 13 0 17 13 4 17 13 5
17 13 6 17 13 9 17 13 13
17 13 14 17 13 15 17 13 18
17 14 0 17 14 1 17 14 2
17 14 4 17 14 9 17 14 10
17 14 11 17 14 13 17 14 18
17 15 0 17 15 2 17 15 3
17 15 5 17 15 6 17 15 9
17 15 11 17 15 12 17 15 14
17 15 15 17 16 1 17 16 7
17 16 10 17 16 16 17 17 0
17 17 2 17 17 4 17 17 5
17 17 6 17 17 7 17 17 8
17 17 9 17 17 11 17 17 13
17 17 14 17 17 15 17 17 16
17 17 17 17 18 0 17 18 1
17 18 3 17 18 4 17 18 5
17 18 6 17 18 7 17 18 9
17 18 10 17 18 12 17 18 13
17 18 14 17 18 15 17 18 16
18 1 5 18 1 7 18 1 8
18 1 14 18 1 16 18 1 17
18 2 7 18 2 8 * 18 2 16 *
18 2 17 18 3 2 18 3 3
18 3 8 18 3 11 18 3 12
18 3 17 18 4 0 * 18 4 1
18 4 4 * 18 4 7 18 4 9
18 4 10 * 18 4 13 18 4 16 *
18 4 18 * 18 6 6 * 18 6 15
18 7 0 18 7 2 18 7 4
18 7 9 18 7 11 18 7 13
18 7 18 18 8 2 * 18 8 3
18 8 8 * 18 8 11 18 8 12 *
18 8 17 18 9 1 18 9 7
18 10 5 18 10 7 18 10 8 *
18 10 14 * 18 10 16 * 18 10 17
18 11 7 18 11 8 18 11 16
18 11 17 18 12 2 * 18 12 3
18 12 8 * 18 12 11 18 12 12 *
18 12 17 18 13 0 18 13 1
18 13 4 18 13 7 18 13 9
18 13 10 18 13 13 18 13 16
18 13 18 18 15 6 18 15 15
18 16 0 * 18 16 2 * 18 16 4 *
18 16 9 18 16 11 18 16 13
18 16 18 * 18 17 2 18 17 3
18 17 8 18 17 11 18 17 12
18 17 17 18 18 2 * 18 18 4 *
18 18 6 * 18 18 8 * 18 18 9
18 18 11 18 18 13 18 18 15
18 18 17
64 MAX ADDS FOR 5561 PALINDROME CLASSES, WITH 937 INTRANSIGENT CLASSES
PALINDROMES GROUPED AS TO THEIR ADD DEPTHS
0-ADD GROUP ALSO INCLUDES INDIVIDUAL PALINDROMES INDICATED BY * ABOVE
ADDS CLASSES ADDS CLASSES ADDS CLASSES ADDS CLASSES
0 8 1 903 2 1087 3 536
4 622 5 410 6 374 7 267
8 217 9 174 10 127 11 127
12 96 13 63 14 53 15 72
16 48 17 44 18 41 19 28
20 23 21 23 22 28 23 16
24 5 25 23 26 18 27 28
28 14 29 8 30 6 31 5
32 6 33 3 34 4 35 5
36 3 37 5 38 1 39 2
45 4 46 6 47 1 50 4
51 6 52 2 53 1 57 4
58 2 59 1 60 1 63 4
64 2