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

1,4

Comments

A352671 gives row lengths.

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

Formula

T(n, 1) = 0.

Example

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]

Prog

(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 }

Crossrefs

Cf. A216789, A352671 (row lengths).

Sequence in context: A137303 A049084 A234580 * A108416 A215395 A338569

Adjacent sequences: A352737 A352738 A352739 * A352741 A352742 A352743

Keyword

nonn,base,tabf

Author

Rémy Sigrist, Mar 31 2022

Status

approved