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A174071
Numbers that can be written as a sum of at least 4 consecutive positive squares.
4
30, 54, 55, 86, 90, 91, 126, 135, 139, 140, 174, 190, 199, 203, 204, 230, 255, 271, 280, 284, 285, 294, 330, 355, 366, 371, 380, 384, 385, 415, 446, 451, 476, 492, 501, 505, 506, 510, 534, 559, 595, 615, 620, 630, 636, 645, 649, 650, 679, 728, 730, 734, 764
OFFSET
1,1
COMMENTS
Numbers of the form m*(6*k^2 + 6*k*m + 2*m^2 - 6*k - 3*m + 1)/6 for some m>=4 and k>=1. - Robert Israel, May 06 2019
LINKS
EXAMPLE
30=1^2+2^2+3^2+4^2, 54=2^2+3^2+4^2+5^2, 55=1^2+2^2+3^2+4^2+5^2, ...
MAPLE
N:= 1000: # to get all terms <= N
Res:= NULL:
for m from 4 while m*(m+1)*(2*m+1)/6 <= N do
for k from 1 do
v:= m*(6*k^2 + 6*k*m + 2*m^2 - 6*k - 3*m + 1)/6;
if v > N then break fi;
Res:= Res, v;
od od:
sort(convert({Res}, list)); Robert Israel, May 06 2019
MATHEMATICA
max=60^2; lst={}; Do[z=n^2+(n+1)^2+(n+2)^2; Do[z+=(n+x)^2; If[z>max, Break[]]; AppendTo[lst, z], {x, 3, Sqrt[max]/2}], {n, Sqrt[max]/2}]; Union[lst]
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by Robert Israel, May 06 2019
STATUS
approved