A362366 Square array A(n, k), n, k >= 0, read by antidiagonals; A(n, k) is the least base >= 2 where the sum n + k can be computed without carry.

2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 5, 3, 2, 2, 2, 3, 3, 2, 2, 2, 4, 2, 3, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 5, 5, 4, 4, 5, 5, 2, 2, 2, 3, 2, 6, 4, 4, 4, 6, 2, 3, 2, 2, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 2, 2, 5, 5, 3, 2, 5, 5, 5, 2, 3, 5, 5, 2

Offset

0,1

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10010

Wolfdieter Lang, Cantor's List of Real Algebraic Numbers of Heights 1 to 7, arXiv:2307.10645 [math.NT], 2023.

Rémy Sigrist, Colored representation of the array for n, k <= 1024 (the color is function of A(n, k), black pixels denote 2's)

Formula

A(n, k) <= max(2, n + k + 1).

A(n, k) = A(k, n).

A(n, 0) = 2.

A(n, n) = A321882(n).

Example

Array A(n, k) begins:
  n\k | 0  1  2  3  4  5  6  7  8  9  10  11  12
  ----+-----------------------------------------
    0 | 2  2  2  2  2  2  2  2  2  2   2   2   2
    1 | 2  3  2  3  2  4  2  3  2  3   2   5   2
    2 | 2  2  5  3  2  2  3  5  2  2   5   5   2
    3 | 2  3  3  3  2  3  5  6  2  3   3   3   2
    4 | 2  2  2  2  3  4  4  4  2  2   2   2   3
    5 | 2  4  2  3  4  4  4  5  2  3   2   5   3
    6 | 2  2  3  5  4  4  5  5  2  2   3   3   5
    7 | 2  3  5  6  4  5  5  5  2  3   3   5   5
    8 | 2  2  2  2  2  2  2  2  6  3   5   5   6
    9 | 2  3  2  3  2  3  2  3  3  3   3   3   3
   10 | 2  2  5  3  2  2  3  3  5  3   3   5   3
   11 | 2  5  5  3  2  5  3  5  5  3   5   5   3
   12 | 2  2  2  2  3  3  5  5  6  3   3   3   3

Prog

(PARI) A(n, k) = { for (b = 2, oo, if (sumdigits(n+k, b) == sumdigits(n, b) + sumdigits(k, b), return (b); ); ); }

Crossrefs

Cf. A321882, A362367.

Sequence in context: A304523 A368541 A020649 * A183024 A067131 A094915

Adjacent sequences: A362363 A362364 A362365 * A362367 A362368 A362369

Keyword

nonn,base,tabl

Author

Rémy Sigrist, Apr 17 2023

Status

approved