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A112510 Least n-bit number whose binary representation's substrings represent the maximal number (A112509(n)) of distinct integers. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
See A112509 for a full explanation and example.
LINKS
2008/9 British Mathematical Olympiad Round 2, Problem 4, Jan 29 2009.
PROG
(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
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Jan 13 2023
CROSSREFS
Cf. A112509 (corresponding maximum), A112511 (greatest n-bit number for which this maximum occurs).
Sequence in context: A159553 A327727 A222970 * A284449 A011949 A350271
KEYWORD
base,nonn
AUTHOR
Rick L. Shepherd, Sep 09 2005
EXTENSIONS
a(21)-a(31) from Joseph Myers, Feb 01 2009
STATUS
approved

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Last modified July 15 12:56 EDT 2024. Contains 374332 sequences. (Running on oeis4.)