A156023 a(n) = n*(n+1)/2 - A112509(n).

0, 0, 1, 3, 5, 8, 11, 14, 18, 22, 26, 31, 36, 41, 47, 53, 59, 65, 72, 79, 86, 93, 100, 108, 116, 124, 132, 141, 150, 159, 168, 177, 186, 196, 206, 216, 226, 237, 248, 259, 270, 281, 292, 303, 315, 327, 339, 351, 363, 376, 389, 401, 414, 427, 440, 453, 467, 481

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; A112509 is the maximum number of substrings representing distinct 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, A156024, A156025. Equals A156024(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