A091460 Greatest size of an arithmetic progression contained as substrings in binary representation of n.

1, 1, 3, 2, 3, 3, 4, 2, 3, 3, 3, 4, 5, 4, 4, 2, 3, 3, 3, 5, 3, 3, 4, 4, 5, 5, 4, 4, 5, 4, 4, 2, 3, 3, 3, 5, 3, 3, 5, 5, 3, 3, 3, 4, 7, 4, 4, 4, 5, 5, 5, 5, 7, 4, 4, 4, 5, 5, 4, 4, 5, 4, 4, 2, 3, 3, 3, 5, 3, 3, 5, 5, 3, 3, 3, 6, 5, 7, 5, 5, 3, 3, 3, 6, 3, 3, 4, 4, 7, 7, 4, 4, 8, 4, 4, 4, 5, 5, 5, 5, 5, 7

Offset: 0

Author

Reinhard Zumkeller, Jan 12 2004

Keywords

• nonn
• base

Comments

a(n) <= A078822(n);

a(A091461(n))=n and a(m)<>n for m < A091461(n).

Examples

			n=28->'11100', {0+k*1: 0<=k<a(28)=5}: bbbb0 => bb1bb => bb10b => b11bb => bb100;
n=29->'11101', {1+k*2: 0<=k<a(29)=4}: bbbb1 => b11bb => bb101 => 111bb.
		

Links

• Álvar Ibeas, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A078822, A007088.