A089998 Smallest square with Hamming weight n (i.e., with exactly n 1's when written in binary).

0, 1, 9, 25, 169, 121, 441, 1521, 2025, 5625, 24025, 47089, 109561, 32761, 393129, 851929, 1540081, 6275025, 15327225, 27258841, 41925625, 127893481, 243204025, 385611769, 998244025, 1979449081, 4823441401, 12870221809, 34324602361

Offset: 0

Author

Reinhard Zumkeller, Nov 20 2003

Keywords

• nonn
• base

Comments

A000120(a(n)) = n.

Links

• Donovan Johnson, Table of n, a(n) for n = 0..60

Crossrefs

Cf. A000290, A089999, A061712, A090001, A231897.

Programs

Mathematica

a = Table[0, {30}]; Do[c = Count[IntegerDigits[n^2, 2], 1]; If[ a[[c + 1]] == 0, a[[c + 1]] = n^2; Print[c, " = ", n^2]], {n, 1, 360000}] (* Robert G. Wilson v, Dec 03 2003 *)
Join[{0},With[{s=DigitCount[Range[400000]^2,2,1]},Flatten[Table[ Position[ s,?(#==n&),1,1],{n,30}]]]^2] (* _Harvey P. Dale, Mar 03 2013 *)

Formula

a(n) = A231897(n)^2. - Hugo Pfoertner, Dec 27 2022

Extensions

More terms from Robert G. Wilson v, Dec 03 2003

Offset corrected by Donovan Johnson, May 01 2012