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A156022
Maximum number of positive numbers represented by substrings of an n-bit number's binary representation
6
1, 2, 4, 6, 9, 12, 16, 21, 26, 32, 39, 46, 54, 63, 72, 82, 93, 105, 117, 130, 144, 159, 175, 191, 208, 226, 245, 264, 284, 305, 327
OFFSET
1,2
COMMENTS
Equivalently, maximum number of distinct substrings starting with a "1" digit.
LINKS
2008/9 British Mathematical Olympiad Round 2, Problem 4, Jan 29 2009.
PROG
(Python)
from itertools import product
def s(w):
return set(w[i:j+1] for i in range(len(w)) if w[i] != "0" for j in range(i, len(w)))
def a(n):
return max(len(s("1"+"".join(b))) for b in product("01", repeat=n-1))
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Jan 13 2023
CROSSREFS
Equals A112509(n)-1 for n >= 2.
Sequence in context: A194250 A024610 A022778 * A224809 A327094 A048171
KEYWORD
nonn,base,more
AUTHOR
Joseph Myers, Feb 01 2009
STATUS
approved