A144016 - OEIS

%I #14 Mar 10 2018 07:13:45

%S 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,

%T 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,

%U 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

%N 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.

%C From _Rémy Sigrist_, Mar 10 2018: (Start)

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

%C See A261467 for the indices of record values.

%C (End)

%H Rémy Sigrist, <a href="/A144016/b144016.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A261461(n) - 1. - _Rémy Sigrist_, Mar 10 2018

%e 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.

%Y Cf. A213629, A261461, A261467.

%K base,nonn

%O 1,2

%A _Leroy Quet_, Sep 07 2008

%E Extended by _Ray Chandler_, Nov 07 2008