A147762 a(n) is the smallest positive integer m with exactly n zeros and exactly n ones in its binary representation and with n represented in binary as a substring of the binary representation of m.

2, 9, 35, 135, 535, 2103, 8255, 32895, 131711, 525695, 2098687, 8395263, 33561599, 134233087, 536887295, 2147516415, 8590229503, 34360360959, 137439608831, 549758566399, 2199026139135, 8796099051519, 35184378380287, 140737540784127, 562950007947263

Offset

1,1

Comments

a(1662) has 1001 digits. - Michael S. Branicky, Feb 18 2023

Links

Michael S. Branicky, Table of n, a(n) for n = 1..1661

Formula

a(n) = 2^(2n-1) + 2^(n-1) - 1 if n is a power of 2; else a(n) = 2^(2n-1) + n*2^m + 2^m - 1 where m = n - 1 - A000120(n). - Michael S. Branicky, Feb 18 2023

Example

6 represented in binary is 110. 2103 represented in binary is 100000110111, which contains exactly six 0's and exactly six 1's and contains 110 as a substring (100000{110}111). Since 2103 is the smallest positive integer that satisfies the conditions, then a(6) = 2103.

Prog

(Python)
def a(n):
    b = bin(n)[2:]
    t = b.rstrip("0")
    if t == "1": return int("1" + "0"*n + "1"*(n-1), 2)
    return int("1" + "0"*(n-b.count("0")) + b + "1"*(n-1-b.count("1")), 2)
print([a(n) for n in range(1, 26)]) # Michael S. Branicky, Feb 18 2023

Crossrefs

Cf. A000120, A023416, A147760, A147761.

Sequence in context: A083141 A001571 A092431 * A077837 A289974 A289782

Adjacent sequences: A147759 A147760 A147761 * A147763 A147764 A147765

Keyword

base,nonn

Author

Leroy Quet, Nov 11 2008

Extensions

Extended by Ray Chandler, Nov 15 2008

a(24) and beyond from Michael S. Branicky, Feb 18 2023

Status

approved