A343934 Irregular triangle read by rows: row n gives the sequence of iterations of k - A006519(k), starting with k=n, until 0 is reached.

1, 2, 3, 2, 4, 5, 4, 6, 4, 7, 6, 4, 8, 9, 8, 10, 8, 11, 10, 8, 12, 8, 13, 12, 8, 14, 12, 8, 15, 14, 12, 8, 16, 17, 16, 18, 16, 19, 18, 16, 20, 16, 21, 20, 16, 22, 20, 16, 23, 22, 20, 16, 24, 16, 25, 24, 16, 26, 24, 16, 27, 26, 24, 16, 28, 24, 16

Offset: 1

Author

Christian Perfect, May 04 2021

Keywords

• nonn
• easy
• tabf

Comments

Row n starts with n, then the highest power of 2 dividing n is subtracted to produce the next entry in the row.

n first appears at position A000788(n)+1.

Examples

			The triangle begins
1
2
3 2
4
5 4
6 4
7 6 4
		

Links

• Peter Kagey, Rows n = 1..1023, flattened

Crossrefs

Cf. A000120 (row widths), A000788, A006519, A129760, A298011 (row sums).

Programs

Mathematica

Table[Most @ NestWhileList[# - 2^IntegerExponent[#, 2] &, n, # > 0 &], {n, 1, 30}] // Flatten (* Amiram Eldar, May 05 2021 *)

Python

def gen_a():
    for n in range(1,100):
        k = n
        while k>0:
            yield k
            k = k & (k-1)
a = gen_a()