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A112510
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Least n-bit number whose binary representation's substrings represent the maximal number (A112509(n)) of distinct integers.
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7
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0, 2, 6, 12, 28, 56, 116, 244, 488, 984, 2008, 4016, 8048, 16240, 32480, 64968, 129992, 261064, 522128, 1044264, 2088552, 4177512, 8371816, 16743632, 33487312, 66976208, 134085072, 268170144, 536340304, 1072680624, 2145361584
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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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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):
if n == 1: return 0
m = -1
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
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CROSSREFS
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Cf. A112509 (corresponding maximum), A112511 (greatest n-bit number for which this maximum occurs).
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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