A275740 Sums of the next n consecutive nonsquare integers.

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

Robert Israel, Table of n, a(n) for n = 0..10000

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

Cf. A000037, A006003, A229183, A027480.

Sequence in context: A212981 A051744 A062443 * A141582 A192692 A182704

Adjacent sequences: A275737 A275738 A275739 * A275741 A275742 A275743

Keyword

nonn,easy

Author

Olivier Gérard, Aug 07 2016

Extensions

Definition clarified by Harvey P. Dale, Jan 04 2024

Status

approved