Digit Block
Let u_(B,b)(n) be the number of digit blocks of a sequence B in the base-b expansion of n. The following table gives the sequence {u_(B)(n)} for a number of blocks B.
B OEIS u_(B,2)(n) for n=1, 2, ...
00 A056973 0,
0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 3, ...
01 A037800 0,
0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, ...
10 A033264 0,
1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, ...
11 A014081 0,
0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 1, 1, 2, 3, 0, ...
000 A056974 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, ...
001 A056975 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, ...
010 A056976 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, ...
011 A056977 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, ...
100 A056978 0,
0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, ...
101 A056979 0,
0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, ...
110 A056980 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, ...
111 A014082 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, ...
See also
Digit Sum, Rudin-Shapiro SequenceExplore with Wolfram|Alpha
WolframAlpha
More things to try:
References
Sloane, N. J. A. Sequences A014081, A014082, A033264, A037800, A056973, A056974, A056975, A056976, A056977, A056978, A056979, and A056980 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Digit BlockCite this as:
Weisstein, Eric W. "Digit Block." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DigitBlock.html