A374448 Irregular table T(n, k), n >= 0, 0 <= k < A089898(n), read by rows; the n-th row lists the numbers m in the range 0..n such that m and n-m can be added without carries in base 10.

0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 10, 0, 1, 10, 11, 0, 1, 2, 10, 11, 12, 0, 1, 2, 3, 10, 11, 12, 13, 0, 1, 2, 3, 4, 10, 11, 12, 13, 14

Offset

0,6

Comments

The n-th row lists the numbers m such that for any k > 0, the k-th rightmost digit of m is <= the k-th rightmost digit of n.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..9077 (rows for n = 0..200 flattened)

Formula

T(n, 0) = 0.

T(n, A089898(n)-1) = n.

T(n, k) + T(n, A089898(n)-1-k) = n.

T(10*n, k) = 10*T(n, k).

Example

Table T(n, k) begins:
  n   n-th row
  --  ---------------------------------
   0  0
   1  0, 1
   2  0, 1, 2
   3  0, 1, 2, 3
   4  0, 1, 2, 3, 4
   5  0, 1, 2, 3, 4, 5
   6  0, 1, 2, 3, 4, 5, 6
   7  0, 1, 2, 3, 4, 5, 6, 7
   8  0, 1, 2, 3, 4, 5, 6, 7, 8
   9  0, 1, 2, 3, 4, 5, 6, 7, 8, 9
  10  0, 10
  11  0, 1, 10, 11
  12  0, 1, 2, 10, 11, 12
  13  0, 1, 2, 3, 10, 11, 12, 13
  14  0, 1, 2, 3, 4, 10, 11, 12, 13, 14

Prog

(PARI) T(n, k, base = 10) = { my (v = 0, p = 1, d, t); while (n, d = n % base; n \= base; t = k % (d+1); k \= (d+1); v += t * p; p *= base; ); return (v); }

Crossrefs

Cf. A002262, A089898, A295989 (base-2 analog).

Sequence in context: A025682 A025691 A002262 * A298486 A189768 A362327

Adjacent sequences: A374445 A374446 A374447 * A374449 A374450 A374451

Keyword

nonn,base,easy,tabf

Author

Rémy Sigrist, Jul 08 2024

Status

approved