A380123 Irregular table T(n, k), n >= 0, k = 1..A380122(n), read by rows; the n-th row lists the integers m (possibly negative) such that the nonzero digits in the nonadjacent form for m appear in the nonadjacent form for n.

0, 0, 1, 0, 2, -1, 0, 3, 4, 0, 4, 0, 1, 4, 5, -2, 0, 6, 8, -1, 0, 7, 8, 0, 8, 0, 1, 8, 9, 0, 2, 8, 10, -5, -4, -1, 0, 11, 12, 15, 16, -4, 0, 12, 16, -4, -3, 0, 1, 12, 13, 16, 17, -2, 0, 14, 16, -1, 0, 15, 16, 0, 16, 0, 1, 16, 17, 0, 2, 16, 18, -1, 0, 3, 4, 15, 16, 19, 20

Offset

0,5

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6724 (rows for n = 0..2^9 flattened)

Joerg Arndt, Matters Computational (The Fxtbook), pages 61-62.

Wikipedia, Non-adjacent form

Formula

T(n, 1) = A184616(n).

T(n, A380122(n)) = n.

Example

Irregular table T(n, k) begins:
  n   n-th row
  --  -----------------------------
   0  0
   1  0, 1
   2  0, 2
   3  -1, 0, 3, 4
   4  0, 4
   5  0, 1, 4, 5
   6  -2, 0, 6, 8
   7  -1, 0, 7, 8
   8  0, 8
   9  0, 1, 8, 9
  10  0, 2, 8, 10
  11  -5, -4, -1, 0, 11, 12, 15, 16
  12  -4, 0, 12, 16
  13  -4, -3, 0, 1, 12, 13, 16, 17
  14  -2, 0, 14, 16
  15  -1, 0, 15, 16
  16  0, 16
.
Irregular table T(n, k) begins in nonadjacent form:
  n      n-th row
  -----  ------------------------------------------
      0  0
      1  0, 1
     10  0, 10
    10T  T, 0, 10T, 100
    100  0, 100
    101  0, 1, 100, 101
   10T0  T0, 0, 10T0, 1000
   100T  T, 0, 100T, 1000
   1000  0, 1000
   1001  0, 1, 1000, 1001
   1010  0, 10, 1000, 1010
  10T0T  T0T, T00, T, 0, 10T0T, 10T00, 1000T, 10000
  10T00  T00, 0, 10T00, 10000

Prog

(PARI) row(n) = { my (r = [0], d, b = 1); while (n, if (n % 2, n -= d = 2 - (n%4); r = concat(r, [v + d*b | v <- r]); ); n /= 2; b *= 2; ); vecsort(r); }

Crossrefs

See A295989 for a similar sequence.

Cf. A184616, A380122.

Sequence in context: A049242 A108887 A337804 * A357368 A193401 A220399

Adjacent sequences: A380113 A380121 A380122 * A380129 A380130 A380131

Keyword

sign,base,tabf,new

Author

Rémy Sigrist, Jan 12 2025

Status

approved