[seqfan] Re: The last digit "d" of a(n) is present in a(n+1+d) -- END

[Eric Angelini]

Duncan Booth has computed the seq (see pgm and table
on rec.puzzles or below):

> 1, 2, 10, 20, 102, 103, 104, 112, 113, 123, 124, 134, 135, 136, 137, 140, 204, 205, 215, 216, 226, 234, 237, 245, 250, 260, 406, 416, 417, 425, 427, 428, 429, 436, 446, 450, 470, 480, 507, 508, 568, 569, 579, 580, 590, 600, 607, 608, 618, 628, 629, 639, 649, 650, 670, 680, 708, 718, 728, 729, 739, 749, 759, 760, 770, 780, 800, 801, 802, 819, 829, 892, 893, 894, 902, 903, 913, 920, 940, 1039, 1093, 1094, 1095, 1096, 1103, 1104, 1114, 1115, 1135, 1139, 1146, 1147, 1148, 1150, 1205, 1206, 1207, 1216, 1217, 1279, ...

I'll submit the seq. to the OEIS in a couple of days.
Best,
(and thanks to all)
É. 

---

from itertools import islice 
def isok(s, needs): 
    s = str(s) 
    for c in needs: 
        if c not in s: 
            return False 
    return True 
def genS(): 
    required = {} 
    n = 1 
    S = 1 
    while 1: 
        obdigits = required.pop(n, "") 
        while not isok(S, obdigits): 
            S += 1 
        yield n,S, obdigits 
        d = S % 10 
        constrain = n+d+1 
        d = str(d) 
        if constrain in required: 
            required[constrain] += d 
        else: 
            required[constrain] = d 
        n += 1 
        S += 1 
if __name__=='__main__': 
    sequence = genS() 
    for n,S,ob in islice(sequence, 100): 
        print n,S,ob 
-------------------------- 
1 1 
2 2 
3 10 1 
4 20 0 
5 102 20 
6 103 
7 104 
8 112 2 
9 113 
10 123 3 
11 124 2 
12 134 4 
13 135 3 
14 136 3 
15 137 
16 140 4 
17 204 40 
18 205 
19 215 5 
20 216 
21 226 6 
22 234 4 
23 237 7 
24 245 5 
25 250 5 
26 260 0 
27 406 640 
28 416 6 
29 417 
30 425 5 
31 427 7 
32 428 
33 429 
34 436 6 
35 446 6 
36 450 5 
37 470 70 
38 480 0 
39 507 70 
40 508 
41 568 86 
42 569 6 
43 579 9 
44 580 
45 590 0 
46 600 0 
47 607 70 
48 608 
49 618 8 
50 628 8 
51 629 
52 639 9 
53 649 9 
54 650 
55 670 70 
56 680 0 
57 708 80 
58 718 8 
59 728 8 
60 729 
61 739 9 
62 749 9 
63 759 9 
64 760 
65 770 0 
66 780 80 
67 800 80 
68 801 80 
69 802 
70 819 91 
71 829 9 
72 892 92 
73 893 9 
74 894 
75 902 2 
76 903 
77 913 3 
78 920 2 
79 940 40 
80 1039 930 
81 1093 93 
82 1094 
83 1095 
84 1096 
85 1103 3 
86 1104 
87 1114 4 
88 1115 
89 1135 53 
90 1139 9 
91 1146 64 
92 1147 4 
93 1148 
94 1150 5 
95 1205 50 
96 1206 
97 1207 
98 1216 6 
99 1217 
100 1279 97 
...