A147760 a(n) is the smallest positive integer m with exactly n ones in its binary representation and with n represented in binary as a substring of the binary representation of m.

1, 5, 7, 39, 47, 111, 127, 1151, 1279, 2815, 3071, 13311, 14335, 30719, 32767, 557055, 589823, 1245183, 1310719, 5505023, 5767167, 12058623, 12582911, 104857599, 109051903, 226492415, 234881023, 973078527, 1006632959, 2080374783, 2147483647, 70866960383

Offset

1,2

Comments

a(3320) has 1001 digits. - Michael S. Branicky, Feb 18 2023

Links

Michael S. Branicky, Table of n, a(n) for n = 1..3319

Formula

a(n) = n*2^m + 2^m - 1 where m = n - A000120(n). - Michael S. Branicky, Feb 18 2023

Example

6 represented in binary is 110. 111 (decimal) represented in binary is 1101111, which contains exactly six 1's and 110 as a substring ({110}1111). Since 111 is the smallest positive integer that satisfies the conditions, then a(6) = 111.

Prog

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

Crossrefs

Cf. A000120, A147761, A147762.

Sequence in context: A006067 A244260 A178428 * A154148 A340818 A242241

Adjacent sequences: A147757 A147758 A147759 * A147761 A147762 A147763

Keyword

base,nonn

Author

Leroy Quet, Nov 11 2008

Extensions

Extended by Ray Chandler, Nov 15 2008

a(31) and beyond from Michael S. Branicky, Feb 18 2023

Status

approved