cp's OEIS Frontend

A111755 Excess of n over a greedy sum of distinct squares.

%I A111755 #13 Oct 17 2018 04:40:44
%S A111755 0,1,2,0,0,1,2,3,0,0,1,2,0,0,1,0,0,1,2,0,0,1,2,3,0,0,1,2,0,0,1,2,3,0,
%T A111755 0,0,0,1,2,0,0,1,2,3,0,0,1,2,0,0,1,2,0,0,1,2,3,0,0,1,2,0,0,0,0,1,2,0,
%U A111755 0,1,2,3,0,0,1,2,0,0,1,0,0,0,1,2,0,0,1,2,3,0,0,1,2,0,0,1,0,0,1,0,0,1,2,0,0
%N A111755 Excess of n over a greedy sum of distinct squares.
%C A111755 Start with the value n and subtract the largest square (not previously used) less than or equal to n to get a new value. Repeat until the value 0 is reached or the square 1 has been subtracted. The resulting value is a(n). It is not hard to prove that a(n) always lies in 0..3 inclusive.
%C A111755 All nonzero terms are one greater than the previous term. - _Iain Fox_, Oct 17 2018
%H A111755 Iain Fox, <a href="/A111755/b111755.txt">Table of n, a(n) for n = 1..10000</a>
%F A111755 a(A003995(n)) = 0. - _Iain Fox_, Oct 17 2018
%e A111755 a(24)=3, since 24 -> 24 - 16 = 8 -> 8 - 4 = 4 -> 4 - 1 = 3.
%t A111755 f[n_] := Block[{s = n, k = Floor@Sqrt@n}, While[k > 0, If[s >= k^2, s -= k^2]; k-- ]; s]; Array[f, 105] (* _Robert G. Wilson v_, Nov 22 2005 *)
%o A111755 (PARI) a(n) = my(s=sqrtint(n)); while(s > 0, if(n >= s^2, n -= s^2); s--); n \\ _Iain Fox_, Oct 17 2018
%Y A111755 Cf. A003995.
%K A111755 easy,nonn
%O A111755 1,3
%A A111755 _John W. Layman_, Nov 21 2005