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

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

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