A063772 a(k^2 + i) = k + a(i) for k >= 0 and 0 <= i <= k * 2; a(0) = 0.

0, 1, 2, 3, 2, 3, 4, 5, 4, 3, 4, 5, 6, 5, 6, 7, 4, 5, 6, 7, 6, 7, 8, 9, 8, 5, 6, 7, 8, 7, 8, 9, 10, 9, 8, 9, 6, 7, 8, 9, 8, 9, 10, 11, 10, 9, 10, 11, 12, 7, 8, 9, 10, 9, 10, 11, 12, 11, 10, 11, 12, 13, 12, 13, 8, 9, 10, 11, 10, 11, 12, 13, 12, 11, 12, 13, 14, 13, 14, 15, 12, 9, 10, 11, 12

Offset: 0

Author

Reinhard Zumkeller, Aug 15 2001

Keywords

• nonn
• look

Comments

a(n^2) = n (by definition).

First difference from A138554 is a(32) = 10 (5^2+2^2+1^2+1^2+1^2), A138554(32) = 8 (4^2+4^2). - Franklin T. Adams-Watters, Jun 25 2015

a(n) is the sum of the roots of the summands when n is expressed as a sum of squares using the greedy algorithm (as in A053610). - Franklin T. Adams-Watters, Jun 30 2015

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A053610, A138554.

Programs

Maple

a:= proc(n)  option remember;
      local k;
      k:= floor(sqrt(n));
      k + procname(n-k^2);
end proc:
a(0):= 0:
map(a, [$0..100]); # Robert Israel, Jun 30 2015

Mathematica

a[0] = 0; a[n_] := a[n] = With[{k = n // Sqrt // Floor}, k + a[n-k^2]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Mar 04 2019 *)