A245563 Table read by rows: row n gives list of lengths of runs of 1's in binary expansion of n, starting with low-order bits.

0, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 3, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 2, 2, 3, 1, 3, 4, 5, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 3, 1, 4, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 2, 2, 2, 3, 2, 3, 1, 3, 1, 3, 2, 3, 4, 1, 4, 5, 6, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1

Offset

0,4

Comments

A formula for A071053(n) depends on this table.

Links

Reinhard Zumkeller, Rows n = 0..1000 of triangle, flattened

Index entries for sequences related to binary expansion of n

Example

Here are the run lengths for the numbers 0 through 21:
0, []
1, [1]
2, [1]
3, [2]
4, [1]
5, [1, 1]
6, [2]
7, [3]
8, [1]
9, [1, 1]
10, [1, 1]
11, [2, 1]
12, [2]
13, [1, 2]
14, [3]
15, [4]
16, [1]
17, [1, 1]
18, [1, 1]
19, [2, 1]
20, [1, 1]
21, [1, 1, 1]

Maple

for n from 0 to 128 do
lis:=[]; t1:=convert(n, base, 2); L1:=nops(t1); out1:=1; c:=0;
for i from 1 to L1 do
if out1 = 1 and t1[i] = 1 then out1:=0; c:=c+1;
elif out1 = 0 and t1[i] = 1 then c:=c+1;
elif out1 = 1 and t1[i] = 0 then c:=c;
elif out1 = 0 and t1[i] = 0 then lis:=[op(lis), c]; out1:=1; c:=0;
fi;
if i = L1 and c>0 then lis:=[op(lis), c]; fi;
od:
lprint(n, lis);
od:

Mathematica

Join@@Table[Length/@Split[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], #2==#1+1&], {n, 0, 100}] (* Gus Wiseman, Nov 03 2019 *)

Prog

(Haskell)
import Data.List (group)
a245563 n k = a245563_tabf !! n !! k
a245563_row n = a245563_tabf !! n
a245563_tabf = [0] : map
   (map length . (filter ((== 1) . head)) . group) (tail a030308_tabf)
-- Reinhard Zumkeller, Aug 10 2014
(Python)
from re import split
A245563_list = [0]
for n in range(1, 100):
....A245563_list.extend(len(d) for d in split('0+', bin(n)[:1:-1]) if d != '')
# Chai Wah Wu, Sep 07 2014

Crossrefs

Row sums = A000120 (the binary weight).

Cf. A245562, A071053.

Cf. A030308, A227736.

Row lengths are A069010.

The version for prime indices (instead of binary indices) is A124010.

Numbers with distinct run-lengths are A328592.

Numbers with equal run-lengths are A164707.

Cf. A003714, A014081, A328166, A328594, A328595, A328596.

Sequence in context: A245562 A304495 A175069 * A356917 A122945 A209972

Adjacent sequences: A245560 A245561 A245562 * A245564 A245565 A245566

Keyword

nonn,base,tabf

Author

N. J. A. Sloane, Aug 10 2014

Status

approved