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

Author

Rémy Sigrist, Jul 08 2024

Keywords

• nonn
• base
• easy
• tabf

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.

Examples

			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
		

Links

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

Crossrefs

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

Programs

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); }

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).