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

1,4

Comments

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

Links

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

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)

Example

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

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 *)

Crossrefs

Cf. A162401.

Sequence in context: A083730 A358272 A008833 * A332012 A365788 A179054

Adjacent sequences: A162397 A162398 A162399 * A162401 A162402 A162403

Keyword

base,nonn

Author

Leroy Quet, Jul 02 2009

Extensions

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

Status

approved