A360963 Triangle T(n, k), n > 0, k = 0..n-1, read by rows: T(n, k) is the least e > 0 such that the binary expansions of n^e and k^e have different lengths.

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3

Offset

1,6

Comments

Leading zeros are ignored (and 0 is assumed to have binary length 0).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10011 (rows for n = 1..141 flattened)

Rémy Sigrist, Colored representation of the first 512 rows

Formula

T(n, 0) = 1.

T(n, n-1) = A183200(n-1) for n > 1.

Example

Triangle T(n, k) begins:
  n\k | 0  1  2  3  4  5  6  7  8  9  10  11  12  13  14
  ----+-------------------------------------------------
    1 | 1
    2 | 1  1
    3 | 1  1  2
    4 | 1  1  1  1
    5 | 1  1  1  1  4
    6 | 1  1  1  1  2  2
    7 | 1  1  1  1  2  2  3
    8 | 1  1  1  1  1  1  1  1
    9 | 1  1  1  1  1  1  1  1  6
   10 | 1  1  1  1  1  1  1  1  4  4
   11 | 1  1  1  1  1  1  1  1  3  3   3
   12 | 1  1  1  1  1  1  1  1  2  2   2   2
   13 | 1  1  1  1  1  1  1  1  2  2   2   2   3
   14 | 1  1  1  1  1  1  1  1  2  2   2   2   3   4
   15 | 1  1  1  1  1  1  1  1  2  2   2   2   3   4   6

Prog

(PARI) T(n, k) = { for (e=1, oo, if (#binary(n^e) != #binary(k^e), return (e))) }

Crossrefs

Cf. A029837, A183200, A360964.

Sequence in context: A025429 A325561 A076250 * A231425 A136713 A224782

Adjacent sequences: A360960 A360961 A360962 * A360964 A360965 A360966

Keyword

nonn,base,tabl

Author

Rémy Sigrist, Feb 27 2023

Status

approved