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 A292690 Square array whose n-th row lists all numbers having n as a substring, read by falling antidiagonals, n >= 0. 11

%I

%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.

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

%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

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Last modified April 18 08:37 EDT 2019. Contains 322209 sequences. (Running on oeis4.)