A147761 a(n) is the smallest positive integer m with exactly n zeros in its binary representation and with n represented in binary as a substring of the binary representation of m.

2, 4, 24, 16, 80, 192, 896, 256, 1152, 2560, 11264, 12288, 53248, 114688, 491520, 65536, 278528, 589824, 2490368, 2621440, 11010048, 23068672, 96468992, 50331648, 209715200, 436207616, 1811939328, 1879048192, 7784628224, 16106127360, 66571993088, 4294967296

Offset

1,1

Comments

a(3315) has 1001 digits. - Michael S. Branicky, Feb 18 2023

Links

Michael S. Branicky, Table of n, a(n) for n = 1..3314

Formula

a(n) = n*2^(n-A023416(n)). - Michael S. Branicky, Feb 18 2023

Example

5 represented in binary is 101. 80 represented in binary is 1010000, which contains exactly five 0's and 101 as a substring ({101}0000). Since 80 is the smallest positive integer that satisfies the conditions, then a(5) = 80.

Prog

(Python)
def a(n): b = bin(n)[2:]; return n << (n - b.count("0"))
print([a(n) for n in range(1, 33)]) # Michael S. Branicky, Feb 18 2023

Crossrefs

Cf. A023416, A147760, A147762.

Sequence in context: A209024 A081680 A269573 * A214299 A090591 A098656

Adjacent sequences: A147758 A147759 A147760 * A147762 A147763 A147764

Keyword

base,nonn

Author

Leroy Quet, Nov 11 2008

Extensions

Extended by Ray Chandler, Nov 15 2008

a(30) and beyond from Michael S. Branicky, Feb 18 2023

Status

approved