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A112511 Greatest n-bit number whose binary representation's substrings represent the maximal number (A112509(n)) of distinct integers. 6
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)
OFFSET

1,2

COMMENTS

See A112509 for a full explanation and example.

LINKS

Table of n, a(n) for n=1..31.

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):

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

CROSSREFS

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

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 January 31 04:27 EST 2023. Contains 359947 sequences. (Running on oeis4.)