A157477 Number of values k < n for which k is a greedy sum of squares.

0, 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 6, 6, 7, 8, 8, 9, 10, 10, 10, 11, 12, 12, 12, 12, 13, 14, 14, 14, 15, 16, 16, 16, 16, 17, 18, 19, 20, 20, 20, 21, 22, 22, 22, 22, 23, 24, 24, 24, 25, 26, 26, 26, 27, 28, 28, 28, 28, 29, 30, 30, 30, 31, 32, 33, 34, 34, 34, 35, 36, 36, 36, 36, 37

Offset

0,3

Links

Table of n, a(n) for n=0..74.

H. L Montgomery and U. M. A. Vorhauer, Greedy sums of distinct squares, Math. Comp. 73 (2004) 493-513, Table 1. [MR2034134].

Maple

greeds := proc(n) local arem, a, j ; arem := n ; a := [] ; while arem > 0 do j := floor(sqrt(arem)) ; a := [op(a), j] ; arem := arem-j^2 ; od: a ; end: isGreedS := proc(n) option remember; local L; L := greeds(n) ; RETURN( nops(L) = nops( convert(L, set)) ) ; end: a := proc(n) local resul, i ; resul := 0 ; for i from 0 to n-1 do if isGreedS(i) then resul := resul+1 ; fi; od: resul ; end: seq(a(n), n=0..80) ;

Mathematica

greeds[n_] := Module[{arem = n, a = {}, j}, While[arem > 0, j = Floor[Sqrt[arem]]; AppendTo[a, j]; arem = arem - j^2]; a];
isGreedS[n_] := isGreedS[n] = Module[{L = greeds[n]}, Length[L] == Length[Union[L]]];
a[n_] := Module[{resul = 0, i}, For[i = 0, i <= n-1, i++, If[isGreedS[i], resul++]]; resul];
Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Nov 29 2023, after R. J. Mathar *)

Crossrefs

Sequence in context: A162351 A087816 A072000 * A248801 A006949 A359536

Adjacent sequences: A157474 A157475 A157476 * A157478 A157479 A157480

Keyword

easy,nonn

Author

R. J. Mathar, Mar 01 2009

Status

approved