A352740 Irregular table T(n, k) read by rows; the n-th row contains, in ascending order, the numbers k < n such that for any base b >= 2, the sum of digits of n and k in base b are different.

0, 0, 0, 2, 0, 3, 0, 4, 0, 0, 4, 6, 0, 6, 7, 0, 7, 8, 0, 8, 0, 6, 8, 9, 10, 0, 11, 0, 12, 0, 10, 12, 0, 8, 12, 14, 0, 13, 15, 0, 14, 15, 16, 0, 15, 16, 0, 16, 17, 18, 0, 19, 0, 20, 0, 0, 12, 16, 18, 20, 21, 22, 0, 23, 0, 24, 0, 18, 24, 0, 14, 21, 24, 25, 26

Offset: 1

Author

Rémy Sigrist, Mar 31 2022

Keywords

• nonn
• base
• tabf

Comments

A352671 gives row lengths.

Examples

			irregular table begins:
     1:    [0]
     2:    [0]
     3:    [0, 2]
     4:    [0, 3]
     5:    [0, 4]
     6:    [0]
     7:    [0, 4, 6]
     8:    [0, 6, 7]
     9:    [0, 7, 8]
    10:    [0, 8]
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10302 (rows for n = 1..2000, flattened)
• Rémy Sigrist, Scatterplot of (x, y) such that x, y <= 1000 and for any base b >= 2, the sum of digits of x and y in base b are different

Crossrefs

Cf. A216789, A352671 (row lengths).

Programs

PARI

row(n) = { my (v=[]); for (k=0, n-1, my (ok=1); for (b=2, max(2, n+1), if (sumdigits(n, b)==sumdigits(k, b), ok=0; break)); if (ok, v=concat(v,k))); v }

Formula

T(n, 1) = 0.