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

1,2

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)

Links

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

Formula

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

Example

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.

Crossrefs

Cf. A213629, A261461, A261467.

Sequence in context: A370820 A261923 A124736 * A354582 A359312 A179868

Adjacent sequences: A144013 A144014 A144015 * A144017 A144018 A144019

Keyword

base,nonn

Author

Leroy Quet, Sep 07 2008

Extensions

Extended by Ray Chandler, Nov 07 2008

Status

approved