A162400 a(n) = the largest square that when represented in binary is a substring within the binary representation of n.

1, 1, 1, 4, 1, 1, 1, 4, 9, 1, 1, 4, 1, 1, 1, 16, 4, 9, 9, 4, 1, 1, 1, 4, 25, 1, 1, 4, 1, 1, 1, 16, 16, 4, 4, 36, 9, 9, 9, 4, 9, 1, 1, 4, 1, 1, 1, 16, 49, 25, 25, 4, 1, 1, 1, 4, 25, 1, 1, 4, 1, 1, 1, 64, 16, 16, 16, 4, 4, 4, 4, 36, 36, 9, 9, 9, 9, 9, 9, 16, 81, 9, 9, 4, 1, 1, 1, 4, 25, 1, 1, 4, 1, 1, 1, 16, 16, 49, 49, 100, 25

Offset: 1

Author

Leroy Quet, Jul 02 2009

Keywords

• base
• nonn

Comments

a(n) = A162401(n)^2.

Examples

			a(8) = 4 since 8 = binary "1000" and the largest square less than or equal to 8, that of 4 = binary "100" appears as the first three bits of "1000". - _Michael De Vlieger_, Nov 04 2017
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..4096

Crossrefs

Cf. A162401.

Programs

Mathematica

Table[Block[{k = n, s}, While[SequenceCount[#, IntegerDigits[Set[s, k^2], 2]] == 0, k--]; s] &@ IntegerDigits[n, 2], {n, 101}] (* Michael De Vlieger, Nov 04 2017 *)

Formula

From David A. Corneth, Nov 04 2017: (Start)

a(n^2) = n^2

a(4*n) = 4*a(n)

a(4*n + 2) = a(2*n + 1). (End)

Extensions

Corrected and extended by Sean A. Irvine, Dec 05 2010