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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.

%I A293869 #26 Mar 01 2024 07:12:15
%S A293869 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,
%T A293869 25,16,7,16,24,32,40,35,26,17,8,17,25,33,41,45,36,27,18,9,18,26,34,42,
%U A293869 50,46,37,28,19,10,19,27,35,43,51,56,47,38,29,100,11
%N A293869 Square array whose n-th row lists all numbers having n as a substring, n >= 1; read by falling antidiagonals.
%H A293869 Rémy Sigrist, <a href="/A293869/b293869.txt">Table of n, a(n) for n = 1..5050</a>
%H A293869 Rémy Sigrist, <a href="/A293869/a293869.pl.txt">Perl program for A293869</a>
%F A293869 T(n, k) = A072484(n, k) for any n > 0 and k = 1..n. - _Rémy Sigrist_, Jan 29 2021
%e A293869 The array starts:
%e A293869    [ 1  10  11  12  13  14  15  16  17  18  19  21  31 ...] = A011531
%e A293869    [ 2  12  20  21  22  23  24  25  26  27  28  29  32 ...] = A011532
%e A293869    [ 3  13  23  30  31  32  33  34  35  36  37  38  39 ...] = A011533
%e A293869    [ 4  14  24  34  40  41  42  43  44  45  46  47  48 ...] = A011534
%e A293869    [ 5  15  25  35  45  50  51  52  53  54  55  56  57 ...] = A011535
%e A293869    [ 6  16  26  36  46  56  60  61  62  63  64  65  66 ...] = A011536
%e A293869    [ 7  17  27  37  47  57  67  70  71  72  73  74  75 ...] = A011537
%e A293869    [ 8  18  28  38  48  58  68  78  80  81  82  83  84 ...] = A011538
%e A293869    [ 9  19  29  39  49  59  69  79  89  90  91  92  93 ...] = A011539
%e A293869    [10 100 101 102 103 104 105 106 107 108 109 110 210 ...] = A293870
%e A293869    [11 110 111 112 113 114 115 116 117 118 119 211 311 ...] = A293871
%e A293869    [12 112 120 121 122 123 124 125 126 127 128 129 212 ...] = A293872
%e A293869    [   ...             ...             ...             ...]
%t A293869 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 *)
%o A293869 (PARI) has=(n,p,m=10^#Str(p))->until(p>n\=10,n%m==p&&return(1))
%o A293869 Mat(vectorv(12,n,a=[];for(k=n,oo,has(k,n)||next;a=concat(a,k);#a>12&&break);a))
%o A293869 (Perl) See Links section.
%Y A293869 Cf. A072484, A292690 (variant starting with row 0).
%Y A293869 Cf. A011540, A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539, A293870, A293871, A293872.
%Y A293869 Cf. A121041, A121022, A121023, A121024, A121025, A121026, A121027, A121028, A121029, A121030, A121031, A121032, A121033, A121034, A121035, A121036, A121037, A121038, A121039, A121040.
%Y A293869 Cf. A179239, A261370.
%Y A293869 Cf. A292451, A292731 (both partially coincide with row 11, but no inclusion relation holds).
%K A293869 nonn,base,tabl,look
%O A293869 1,2
%A A293869 _M. F. Hasler_, Oct 18 2017