A390926 Square array read by upward diagonals: A(n,k) is the position of the k-th occurrence of the decimal string n in the infinite Champernowne word 123456789101112... (A033307).

1, 2, 10, 3, 15, 12, 4, 17, 30, 13, 5, 19, 37, 32, 14, 6, 21, 39, 50, 34, 16, 7, 23, 41, 59, 52, 35, 18, 8, 25, 43, 61, 70, 54, 36, 20, 9, 27, 45, 63, 81, 72, 56, 38, 22, 10, 29, 47, 65, 83, 90, 74, 57, 40, 24, 12, 190, 49, 67, 85, 103, 92, 76, 58, 42, 26, 1

Offset

1,2

Comments

Positions are counted from 1 (i.e., as if the offset of A033307 was 1).

Links

Sean A. Irvine, Table of n, a(n) for n = 1..1000

Example

The array begins:
   1  10  12  13  14  16  18  20  22  24  26  28
   2  15  30  32  34  35  36  38  40  42  44  46
   3  17  37  50  52  54  56  57  58  60  62  64
   4  19  39  59  70  72  74  76  78  79  80  82
   5  21  41  61  81  90  92  94  96  98 100 101
   6  23  43  63  83 103 110 112 114 116 118 120
   7  25  45  65  85 105 125 130 132 134 136 138
   8  27  47  67  87 107 127 147 150 152 154 156
   9  29  49  69  89 109 129 149 169 170 172 174
  10 190 193 196 199 202 205 208 211 214 217 221
  12  13 195 220 223 224 225 226 229 232 235 238
   1  14  33 227 250 253 256 259 262 265 268 271
Note the position of the first occurrence of 11 is at position 12 (not 11) and the first occurrence of 12 is at position 1 (and not 12 or 14).

Crossrefs

Cf. A007376, A033307, A031297 (column 1), A031288 (row 1), A031289 (row 2), ..., A031296 (row 9).

Sequence in context: A379401 A252758 A249917 * A176577 A247476 A245062

Adjacent sequences: A390923 A390924 A390925 * A390927 A390928 A390929

Keyword

nonn,base

Author

Sean A. Irvine, Jan 29 2026

Status

approved