A293869
Square array whose n-th row lists all numbers having n as a substring, n >= 1; read by falling antidiagonals.
Original entry on oeis.org
1, 10, 2, 11, 12, 3, 12, 20, 13, 4, 13, 21, 23, 14, 5, 14, 22, 30, 24, 15, 6, 15, 23, 31, 34, 25, 16, 7, 16, 24, 32, 40, 35, 26, 17, 8, 17, 25, 33, 41, 45, 36, 27, 18, 9, 18, 26, 34, 42, 50, 46, 37, 28, 19, 10, 19, 27, 35, 43, 51, 56, 47, 38, 29, 100, 11
Offset: 1
The array starts:
[ 1 10 11 12 13 14 15 16 17 18 19 21 31 ...] = A011531
[ 2 12 20 21 22 23 24 25 26 27 28 29 32 ...] = A011532
[ 3 13 23 30 31 32 33 34 35 36 37 38 39 ...] = A011533
[ 4 14 24 34 40 41 42 43 44 45 46 47 48 ...] = A011534
[ 5 15 25 35 45 50 51 52 53 54 55 56 57 ...] = A011535
[ 6 16 26 36 46 56 60 61 62 63 64 65 66 ...] = A011536
[ 7 17 27 37 47 57 67 70 71 72 73 74 75 ...] = A011537
[ 8 18 28 38 48 58 68 78 80 81 82 83 84 ...] = A011538
[ 9 19 29 39 49 59 69 79 89 90 91 92 93 ...] = A011539
[10 100 101 102 103 104 105 106 107 108 109 110 210 ...] = A293870
[11 110 111 112 113 114 115 116 117 118 119 211 311 ...] = A293871
[12 112 120 121 122 123 124 125 126 127 128 129 212 ...] = A293872
[ ... ... ... ...]
Cf.
A011540,
A011531,
A011532,
A011533,
A011534,
A011535,
A011536,
A011537,
A011538,
A011539,
A293870,
A293871,
A293872.
Cf.
A121041,
A121022,
A121023,
A121024,
A121025,
A121026,
A121027,
A121028,
A121029,
A121030,
A121031,
A121032,
A121033,
A121034,
A121035,
A121036,
A121037,
A121038,
A121039,
A121040.
Cf.
A292451,
A292731 (both partially coincide with row 11, but no inclusion relation holds).
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Block[{d = 15, q, a, s}, a = Table[q = n-1; s = IntegerString[n]; Table[While[StringFreeQ[IntegerString[++q], s]]; q, d-n+1], {n, d}]; Table[a[[n, k-n+1]], {k, d}, {n, k}]] (* Paolo Xausa, Mar 01 2024 *)
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has=(n,p,m=10^#Str(p))->until(p>n\=10,n%m==p&&return(1))
Mat(vectorv(12,n,a=[];for(k=n,oo,has(k,n)||next;a=concat(a,k);#a>12&&break);a))
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See Links section.
A337918
Rearrangement of natural numbers so that next n numbers contain n as substring.
Original entry on oeis.org
1, 2, 12, 3, 13, 23, 4, 14, 24, 34, 5, 15, 25, 35, 45, 6, 16, 26, 36, 46, 56, 7, 17, 27, 37, 47, 57, 67, 8, 18, 28, 38, 48, 58, 68, 78, 9, 19, 29, 39, 49, 59, 69, 79, 89, 10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119
Offset: 1
As a triangle, the first rows are:
1: 1
2: 2, 12
3: 3, 13, 23
4: 4, 14, 24, 34
5: 5, 15, 25, 35, 45
6: 6, 16, 26, 36, 46, 56
7: 7, 17, 27, 37, 47, 57, 67
8: 8, 18, 28, 38, 48, 58, 68, 78
9: 9, 19, 29, 39, 49, 59, 69, 79, 89
10: 10, 100, 101, 102, 103, 104, 105, 106, 107, 108
11: 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119
12: 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 212, 312
A072483
Triangle read by rows: The n-th row contains the smallest n increasing numbers larger than the last term of the previous row, which contain the string of digits of n.
Original entry on oeis.org
1, 2, 12, 13, 23, 30, 34, 40, 41, 42, 45, 50, 51, 52, 53, 56, 60, 61, 62, 63, 64, 67, 70, 71, 72, 73, 74, 75, 78, 80, 81, 82, 83, 84, 85, 86, 89, 90, 91, 92, 93, 94, 95, 96, 97, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117
Offset: 1
The 6th row contains the 6 smallest numbers > 53 which contain the digit 6. The 10th row contains the 10 smallest numbers > 97 which contain the string "10".
The triangle starts
1
2 12
13 23 30
34 40 41 42
45 50 51 52 53
56 60 61 62 63 64
67 70 71 72 73 74 75
78 80 81 82 83 84 85 86
89 90 91 92 93 94 95 96 97
100 ...
A072485
n-th number that includes the substring [n] in its decimal expansion.
Original entry on oeis.org
1, 12, 23, 34, 45, 56, 67, 78, 89, 108, 119, 129, 213, 314, 415, 516, 617, 718, 819, 920, 1021, 1220, 1223, 1240, 1251, 1262, 1273, 1284, 1295, 1306, 1317, 1328, 1433, 1349, 1435, 1536, 1637, 1738, 1839, 1940, 2041, 2142, 2243, 2441, 2445, 2460, 2471, 2482, 2493, 2504, 2515, 2526, 2537, 2548
Offset: 1
Leading diagonal of triangle defined in
A072484.
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N:= 100: count:= 0: R:= {$1..N}:
V:= Vector(N):
for n from 1 while count < N do
Q:= map(proc(t) local i; seq(t mod 10^i,i=1..1+ilog10(t)) end proc,
{seq(floor(n/10^i), i=0..ilog10(n))}) intersect R;
for m in Q do
V[m]:= V[m]+1;
if V[m] = m then A[m]:= n; count:= count+1 fi
od;
od:
seq(A[i],i=1..N); # Robert Israel, Sep 25 2019
Showing 1-4 of 4 results.
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