A245562 Table read by rows: row n gives list of lengths of runs of 1's in binary expansion of n, starting with high-order bits.

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

Offset: 0

Author

N. J. A. Sloane, Aug 10 2014

Keywords

• nonn
• base
• tabf
• easy

Comments

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

Examples

			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, [1, 2]
12, [2]
13, [2, 1]
14, [3]
15, [4]
16, [1]
17, [1, 1]
18, [1, 1]
19, [1, 2]
20, [1, 1]
21, [1, 1, 1]
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..2770
• N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 2015

Crossrefs

Row sums = A000120 (the binary weight).

Cf. A245563, A071053.

Programs

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:=[c,op(lis)]; out1:=1; c:=0;
   fi;
   if i = L1 and c>0 then lis:=[c,op(lis)]; fi;
                   od:
lprint(n,lis);
od:

PARI

row(n)=my(v=List(),k); while(n, n>>=valuation(n,2); listput(v, k=valuation(n+1,2)); n>>=k); Vecrev(v) \\ Charles R Greathouse IV, Oct 21 2016

Python

from re import split
A245562_list = [0]
for n in range(1,100):
    A245562_list.extend(len(d) for d in split('0+',bin(n)[2:]) if d != '')
# Chai Wah Wu, Sep 07 2014