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A245562
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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.
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12
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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A formula for A071053(n) depends on this table.
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LINKS
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EXAMPLE
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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]
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MAPLE
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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:
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PROG
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(Python)
from re import split
for n in range(1, 100):
....A245562_list.extend(len(d) for d in split('0+', bin(n)[2:]) if d != '')
(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
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CROSSREFS
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Row sums = A000120 (the binary weight).
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KEYWORD
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nonn,base,tabf,easy
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AUTHOR
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STATUS
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approved
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