A144016 a(n) = the largest positive integer m such that the binary representations of all positive integers <= m are found within the binary representation of n.

1, 2, 1, 2, 2, 3, 1, 2, 2, 2, 3, 4, 3, 3, 1, 2, 2, 2, 4, 2, 2, 3, 3, 4, 4, 3, 3, 4, 3, 3, 1, 2, 2, 2, 4, 2, 2, 4, 4, 2, 2, 2, 3, 6, 3, 3, 3, 4, 4, 4, 4, 6, 3, 3, 3, 4, 4, 3, 3, 4, 3, 3, 1, 2, 2, 2, 4, 2, 2, 4, 4, 2, 2, 2, 5, 4, 6, 4, 4, 2, 2, 2, 5, 2, 2, 3, 3, 6, 6, 3, 3, 7, 3, 3, 3, 4, 4, 4, 4, 4, 6, 4, 4, 6, 6

Offset: 1

Author

Leroy Quet, Sep 07 2008

Keywords

• base
• nonn

Comments

From Rémy Sigrist, Mar 10 2018: (Start)

a(n) is the greatest k <= n such that A213629(n, i) > 0 for i = 1..k.

See A261467 for the indices of record values.

(End)

Examples

			44 in binary is 101100. In this string we find 1 (1 in decimal): (1)01100; 10 (2 in decimal): (10)1100; 11 (3 in decimal): 10(11)00; 100 (4 in decimal): 101(100); 101 (5 in decimal): (101)100; and 110 (6 in decimal): 10(110)0; but not 111 (7 in decimal). So a(44) = 6.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A213629, A261461, A261467.

Formula

a(n) = A261461(n) - 1. - Rémy Sigrist, Mar 10 2018

Extensions

Extended by Ray Chandler, Nov 07 2008