A340547 - OEIS

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A340547

Square array, read by ascending antidiagonals, where row n gives all solutions n > 0 to A000120(n+1) = A000120((n+1)*k), A000120 is the Hamming weight.

1, 1, 2, 1, 2, 4, 1, 2, 3, 8, 1, 2, 4, 4, 16, 1, 2, 4, 8, 6, 32, 1, 2, 3, 8, 16, 8, 64, 1, 2, 3, 4, 13, 32, 11, 128, 1, 2, 4, 4, 6, 16, 64, 12, 256, 1, 2, 2, 8, 5, 8, 26, 128, 16, 512, 1, 2, 4, 8, 16, 6, 11, 32, 256, 22, 1024

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

OFFSET

1,3

COMMENTS

Solutions to related equation A000120(k) = A000120(k*n) are A340351.

The same sequence without leading ones and only odd solutions is A340441.

LINKS

Table of n, a(n) for n=1..66.

FORMULA

T(2n, ...) = 2^{0,1,2,...}, 2^{0,1,2,...} * row n of A340441.

T(4n+1, ...) = 2^{0,1,2,...}, 2^{0,1,2,...} * row n of A340441.

T(2^n, ...) = 2^{0,1,2,...}.

EXAMPLE

Eight initial terms of rows 1-8 are listed below:

1: 1, 2, 4, 8, 16, 32, 64, 128, ...

2: 1, 2, 3, 4, 6, 8, 11, 12, ...

3: 1, 2, 4, 8, 16, 32, 64, 128, ...

4: 1, 2, 4, 8, 13, 16, 26, 32, ...

5: 1, 2, 3, 4, 6, 8, 11, 12, ...

6: 1, 2, 3, 4, 5, 6, 7, 8, ...

7: 1, 2, 4, 8, 16, 32, 64, 128, ...

8: 1, 2, 4, 8, 16, 32, 57, 64, ...

T(3,4) = 8 because: (3+1) in binary is 100 and (3*1)*8 = 32 in binary is 100000, both have 1 bit set to 1.

CROSSREFS

Cf. A000120, A340351, A340069, A340441.

Cf. A263132 (superset of 1st row), A007583 (1st row), A299960 (2nd row).

Sequence in context: A174843 A253572 A141539 * A376033 A327844 A243851

Adjacent sequences: A340544 A340545 A340546 * A340548 A340549 A340550

KEYWORD

nonn,base,tabl

AUTHOR

Thomas Scheuerle, Jan 11 2021

STATUS

approved