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A293869
Square array whose n-th row lists all numbers having n as a substring, n >= 1; read by falling antidiagonals.
14
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
1,2
LINKS
FORMULA
T(n, k) = A072484(n, k) for any n > 0 and k = 1..n. - Rémy Sigrist, Jan 29 2021
EXAMPLE
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
[ ... ... ... ...]
MATHEMATICA
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 *)
PROG
(PARI) 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))
(Perl) See Links section.
CROSSREFS
Cf. A072484, A292690 (variant starting with row 0).
Cf. A292451, A292731 (both partially coincide with row 11, but no inclusion relation holds).
Sequence in context: A341816 A339206 A274606 * A365625 A323821 A351840
KEYWORD
nonn,base,tabl,look
AUTHOR
M. F. Hasler, Oct 18 2017
STATUS
approved