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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.
0
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
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.
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. A263132 (superset of 1st row), A007583 (1st row), A299960 (2nd row).
Sequence in context: A174843 A253572 A141539 * A376033 A327844 A243851
KEYWORD
nonn,base,tabl
AUTHOR
Thomas Scheuerle, Jan 11 2021
STATUS
approved