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A275740
Sums of the next n consecutive nonsquare integers.
1
0, 2, 8, 21, 46, 83, 136, 210, 306, 426, 575, 758, 972, 1223, 1519, 1855, 2236, 2669, 3156, 3694, 4290, 4956, 5678, 6467, 7332, 8269, 9278, 10368, 11548, 12804, 14148, 15593, 17126, 18753, 20485, 22325, 24262, 26308, 28481, 30756, 33148
OFFSET
0,2
COMMENTS
Row sums of nonsquare integers (A000037), seen as a regular triangle:
.
2 | 2,
8 | 3, 5,
21 | 6, 7, 8,
46 | 10, 11, 12, 13,
83 | 14, 15, 17, 18, 19,
136 | 20, 21, 22, 23, 24, 26,
210 | 27, 28, 29, 30, 31, 32, 33,
306 | 34, 35, 37, 38, 39, 40, 41, 42,
...
The equivalent for all integers are A006003 (starting from 1), A229183 (starting from 2) and A027480 (starting from 0).
There are several sequences close to nonsquares whose sum of groups of n terms starts like this sequence, notably A028761, A158276, A167759.
LINKS
MAPLE
R:= 0: s:= 1:
for n from 1 to 100 do
if floor(sqrt(s+n)) = floor(sqrt(s)) then
R:= R, n*s + n*(n+1)/2; s:= s+n;
else
R:= R, n*s + n*(n+1)/2 - floor(sqrt(s+n))^2 + s+n+1; s:= s+n+1;
fi
od:
R; # Robert Israel, Oct 02 2022
MATHEMATICA
Table[Sum[
i + Floor[1/2 + Sqrt[i]], {i, n (n - 1)/2 + 1, (n + 1) (n)/2}], {n,
0, 40}]
Join[{0}, Module[{nn=1000, nsi, len}, nsi=Select[Range[nn], !IntegerQ[Sqrt[#]]&]; len=Floor[ (Sqrt[ 8*Length[nsi]+1]-1)/2]; Total/@TakeList[nsi, Range[len]]]] (* Harvey P. Dale, Jan 04 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, Aug 07 2016
EXTENSIONS
Definition clarified by Harvey P. Dale, Jan 04 2024
STATUS
approved