A292690 - OEIS

%I #11 Mar 01 2024 07:14:28

%S 0,10,1,20,10,2,30,11,12,3,40,12,20,13,4,50,13,21,23,14,5,60,14,22,30,

%T 24,15,6,70,15,23,31,34,25,16,7,80,16,24,32,40,35,26,17,8,90,17,25,33,

%U 41,45,36,27,18,9,100,18,26,34,42,50,46,37,28,19,10

%N Square array whose n-th row lists all numbers having n as a substring, read by falling antidiagonals, n >= 0.

%C This array starts with row 0, see A293869 for the variant which starts with row 1.

%H Paolo Xausa, <a href="/A292690/b292690.txt">Table of n, a(n) for n = 0..11324</a> (first 150 antidiagonals).

%e The array starts:

%e    [ 0  10  20  30  40  50  60  70  80  90 100 101 102 ...] = A011540

%e    [ 1  10  11  12  13  14  15  16  17  18  19  21  31 ...] = A011531

%e    [ 2  12  20  21  22  23  24  25  26  27  28  29  32 ...] = A011532

%e    [ 3  13  23  30  31  32  33  34  35  36  37  38  39 ...] = A011533

%e    [ 4  14  24  34  40  41  42  43  44  45  46  47  48 ...] = A011534

%e    [ 5  15  25  35  45  50  51  52  53  54  55  56  57 ...] = A011535

%e    [ 6  16  26  36  46  56  60  61  62  63  64  65  66 ...] = A011536

%e    [ 7  17  27  37  47  57  67  70  71  72  73  74  75 ...] = A011537

%e    [ 8  18  28  38  48  58  68  78  80  81  82  83  84 ...] = A011538

%e    [ 9  19  29  39  49  59  69  79  89  90  91  92  93 ...] = A011539

%e    [10 100 101 102 103 104 105 106 107 108 109 110 210 ...] = A293870

%e    [11 110 111 112 113 114 115 116 117 118 119 211 311 ...] = A293871

%e    [12 112 120 121 122 123 124 125 126 127 128 129 212 ...] = A293872

%e    [   ...             ...             ...             ...]

%t Block[{d = 15, q, a, s}, a = Table[q = n-1; s = IntegerString[n]; Table[While[StringFreeQ[IntegerString[++q], s]]; q, d-n], {n, 0, d-1}]; Table[a[[n+1, k-n]], {k, d}, {n, 0, k-1}]] (* _Paolo Xausa_, Mar 01 2024 *)

%o (PARI) has(n,p,m=10^#Str(p))=until(p+!p>n\=10,n%m==p&&return(1))

%o Mat(vectorv(12,n,a=[];for(k=n--,oo,has(k,n)||next;a=concat(a,k);#a>12&&break);a))

%o for(i=1,11,for(j=1,i,print1(%[j,i-j+1]","))) \\ Read by antidiagonals

%Y Cf. A293869.

%Y Cf. A011540, A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539: rows 0 - 9.

%Y Cf.  A293870, A293871, A293872, A293873, A293874, A293875, A293876, A293877, A293878, A293879, A293880: rows 10 .. 20.

%Y Cf. A121041, A121022, A121023, A121024, A121025, A121026, A121027, A121028, A121029, A121030, A121031, A121032, A121033, A121034, A121035, A121036, A121037, A121038, A121039, A121040: subsequences of the above, only multiples of the pattern p.

%K nonn,base,tabl

%O 0,2

%A _M. F. Hasler_, Oct 18 2017