A133851 Sloping binary representation of powers of 4 (A000302), slope = -1 .

1, 0, 0, 4, 0, 0, 16, 0, 0, 64, 0, 0, 256, 0, 0, 1024, 0, 0, 4096, 0, 0, 16384, 0, 0, 65536, 0, 0, 262144, 0, 0, 1048576, 0, 0, 4194304, 0, 0, 16777216, 0, 0, 67108864, 0, 0, 268435456, 0, 0, 1073741824, 0, 0, 4294967296, 0, 0, 17179869184, 0, 0

Offset: 0

Author

Philippe Deléham, Jan 06 2008

Keywords

• base
• nonn

Examples

			When powers of 4 are written in binary (see A098608), under each other as:
0000000000001 (1)
0000000000100 (4)
0000000010000 (16)
0000001000000 (64)
0000100000000 (256)
0010000000000 (1024)
1000000000000 (4096)
and one collects their bits from the column=0 to NW-direction (from the least to the most significant end), one gets 1 (1), 00 (0), 000 (0), 0100 (4), 00000 (0), 000000 (0), 0010000 (16), etc. (see 0105033 for similar transformation done on nonnegative integers)
		

Crossrefs

Cf. A037095, A077957, A105033, A000302, A098608, A102370(sloping binary numbers).

Formula

a(3n) = A000302(n), a(3n+1) = a(3n+2) = 0. - Alois P. Heinz, Dec 10 2020