A112510 Least n-bit number whose binary representation's substrings represent the maximal number (A112509(n)) of distinct integers.

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

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):
    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).

A078822, A122953, A156022, A156023, A156024, A156025. [From Joseph Myers, Feb 01 2009]

Sequence in context: A159553 A327727 A222970 * A284449 A011949 A350271

Adjacent sequences: A112507 A112508 A112509 * A112511 A112512 A112513

Keyword

base,nonn

Author

Rick L. Shepherd, Sep 09 2005

Extensions

a(21)-a(31) from Joseph Myers, Feb 01 2009

Status

approved