A361674 - OEIS

A361674

Irregular triangle T(n, k), n >= 0, k = 1..2^A092339(n), read by rows; the n-th row lists the numbers k such that n appears in the k-th row of A361644.

0, 1, 2, 2, 3, 4, 5, 5, 5, 6, 4, 5, 6, 7, 8, 9, 10, 11, 9, 10, 10, 10, 11, 10, 11, 12, 13, 10, 13, 9, 10, 13, 14, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 17, 18, 21, 22, 18, 21, 18, 19, 20, 21, 20, 21, 21, 21, 22, 20, 21, 22, 23, 20, 21, 22, 23, 24, 25, 26, 27

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

In other words, the n-th row contains the numbers k with the same binary length as n and for any i >= 0, if the i-th bit and the (i+1)-th bit in n are different then they are also different in k (i = 0 corresponding to the least significant bit).

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..9841 (rows for n = 0..511 flattened)

FORMULA

T(n, 1) = A361645(n).

T(n, 2^A092339(n)) = A361676(n).

EXAMPLE

Triangle T(n, k) begins (in decimal and in binary):

n n-th row bin(n) n-th row in binary

-- -------------- ------ ----------------------

0 0 0 0

1 1 1 1

2 2 10 10

3 2, 3 11 10, 11

4 4, 5 100 100, 101

5 5 101 101

6 5, 6 110 101, 110

7 4, 5, 6, 7 111 100, 101, 110, 111

8 8, 9, 10, 11 1000 1000, 1001, 1010, 1011

9 9, 10 1001 1001, 1010

10 10 1010 1010

11 10, 11 1011 1010, 1011

12 10, 11, 12, 13 1100 1010, 1011, 1100, 1101

13 10, 13 1101 1010, 1101

14 9, 10, 13, 14 1110 1001, 1010, 1101, 1110

PROG

(PARI) row(n) = { my (r = [n], m); for (e = 1, exponent(n), if (bittest(n, e-1)==bittest(n, e), m = 2^e-1; r = concat(r, [bitxor(v, m) | v <- r]); ); ); vecsort(r); }

CROSSREFS

Cf. A361644, A361645, A361676.

Sequence in context: A069928 A135585 A081094 * A054633 A327982 A377983

Adjacent sequences: A361671 A361672 A361673 * A361675 A361676 A361677

KEYWORD

nonn,base,tabf

AUTHOR

Rémy Sigrist, Mar 20 2023

STATUS

approved