A156024 a(n) = n*(n+1)/2 - A156022(n).

0, 1, 2, 4, 6, 9, 12, 15, 19, 23, 27, 32, 37, 42, 48, 54, 60, 66, 73, 80, 87, 94, 101, 109, 117, 125, 133, 142, 151, 160, 169, 178, 187, 197, 207, 217, 227, 238, 249, 260, 271, 282, 293, 304, 316, 328, 340, 352, 364, 377, 390, 402, 415, 428, 441, 454, 468, 482

Offset: 1

Author

Joseph Myers, Feb 01 2009

Keywords

• nonn
• base

Comments

n(n+1)/2 is the total number of nonempty substrings of an n-bit binary number; A156022 is the maximum number of substrings representing distinct positive integers.

Links

• Martin Fuller, Table of n, a(n) for n = 1..80
• 2008/9 British Mathematical Olympiad Round 2, Problem 4, Jan 29 2009.

Crossrefs

Cf. A000217, A078822, A112509, A112510, A112511, A122953, A156022, A156023, A156025.

Equals A156023(n)+1 for n >= 2.

Formula

c_1 + o(1) <= a(n)/n^1.5 <= c_2 + o(1) for some positive constants c_1 and c_2; it seems likely a(n)/n^1.5 tends to some positive constant limit.

Extensions

a(32) onwards from Martin Fuller, Jul 24 2025