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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A212981 A051744 A062443 * A141582 A192692 A182704
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, Aug 07 2016
EXTENSIONS
Definition clarified by Harvey P. Dale, Jan 04 2024
STATUS
approved

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Last modified May 20 11:25 EDT 2024. Contains 372712 sequences. (Running on oeis4.)