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A112511
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Greatest n-bit number whose binary representation's substrings represent the maximal number (A112509(n)) of distinct integers.
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6
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1, 2, 6, 14, 29, 61, 123, 244, 500, 1004, 2009, 4057, 8121, 16243, 32627, 65267, 130535, 261066, 523210, 1046474, 2092954, 4185909, 8371816, 16760424, 33521256, 67042536, 134085073, 268302801, 536607185, 1073214417, 2146428840
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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See A112509 for a full explanation and example.
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LINKS
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Table of n, a(n) for n=1..31.
2008/9 British Mathematical Olympiad Round 2, Problem 4, Jan 29 2009.
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PROG
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(Python)
from itertools import product
def c(w):
return len(set(w[i:j+1] for i in range(len(w)) if w[i] != "0" for j in range(i, len(w)))) + int("0" in w)
def a(n):
m, argm = -1, None
for b in product("01", repeat=n-1):
v = c("1"+"".join(b))
if v >= m:
m, argm = v, int("1"+"".join(b), 2)
return argm
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Jan 13 2023
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CROSSREFS
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Cf. A112509 (corresponding maximum), A112510 (least n-bit number for which this maximum occurs).
A078822, A122953, A156022, A156023, A156024, A156025. [From Joseph Myers, Feb 01 2009]
Sequence in context: A169948 A192705 A123991 * A143702 A063452 A009299
Adjacent sequences: A112508 A112509 A112510 * A112512 A112513 A112514
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KEYWORD
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base,nonn
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AUTHOR
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Rick L. Shepherd, Sep 09 2005
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EXTENSIONS
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a(21)-a(31) from Joseph Myers, Feb 01 2009
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STATUS
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approved
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