A181176 The minimum absolute value obtainable by partitioning the first n consecutive integers into two sets and subtracting the two sums of the sets.

0, 1, 1, 0, 2, 3, 1, 2, 6, 3, 1, 6, 6, 1, 5, 10, 4, 3, 11, 8, 0, 9, 13, 4, 6, 17, 9, 2, 14, 15, 3, 10, 22, 9, 5, 20, 16, 1, 15, 24, 8, 9, 27, 16, 2, 21, 25, 6, 14, 35, 15, 6, 28, 25, 3, 20, 36, 13, 11, 36, 24, 1, 27, 36, 10, 17, 45, 22, 6, 35, 35, 6, 24, 49, 19, 12, 44, 33, 1, 32, 48, 15, 19

Offset

0,5

Comments

a(n)=0 for n = 0, 3, 20, 119, 696, 4059, 23660, 137903, 803760, ..., . A001652

a(n)=1 for n = 1, 2, 6, 10, 13, 37, 61, 78, 218, 358, 457, 1273, 2089, 2666, 7422, ..., .

a(n)=2 for n = 4, 7, 27, 44, 160, 259, 935, 1512, 5452, 8815, ..., .

a(n)=3 for n = 5, 9, 17, 30, 54, 102, 177, 317, 597, 1034, 1850, 3482, 6029, 10785, ..., .

a(n)=4 for n = 16, 23, 95, 136, 556, 795, 3243, 4636, ..., .

a(n)=5 for n = 14, 34, 85, 201, 498, 1174, 2905, 6845, ..., .

a(n)=6 for n = 8, 11, 12, 24, 47, 51, 68, 71, 143, 276, 300, 399, 416, 836, 1611, ..., .

First occurrence of k beginning with 0, or -1 if no such value is known: 0, 1, 4, 5, 16, 14, 8, -1, 19, 21, 15, 18, 75, 22, 28, 29, ..., .

Values that appear to be missing in the sequence: 7, 18, 23, 31, 37, 38, 40, 47, 52, 59, 67, 68, 70, 73, 83, 86, 88, 92, 98, 102, ..., .

Sequence records by value: 0, 1, 2, 3, 6, 10, 11, 13, 17, 22, 24, 27, 35, 36, 45, 49, 54, 63,. 74,. 75,. 82,. 90, ..., .

Sequence records by index: 0, 1, 4, 5, 8, 15, 18, 22, 25, 32, 39, 42, 49, 56, 66, 73, 83, 90, 107, 114, 124, 131, ..., .

Links

Table of n, a(n) for n=0..82.

Example

a(0)=0
a(1)=1
a(2)=1=2-1
a(3)=0=3-(2+1)
a(4)=2=|4-(3+2+1)|
a(5)=3=5+4-(3+2+1)
a(6)=1=6+5-(4+3+2+1)
a(7)=2=7+6-(5+4+3+2+1)
a(8)=6=8+7+6-(5+4+3+2+1)

Mathematica

tri[n_] := n (n + 1)/2; f[n_] := Block[{d, k = 0, mx = Infinity}, While[k < n + 1, d = Abs[ tri@n - 2 tri@k]; If[d < mx, mx = d]; k++ ]; mx]; Array[f, 100, 0]
Join[{0}, Table[Min[Flatten[Table[Abs[Differences[(Total/@TakeDrop[Range[n], k])]], {k, n}]]], {n, 90}]] (* Harvey P. Dale, Mar 08 2023 *)

Crossrefs

Cf. A181177.

Sequence in context: A307668 A308173 A256910 * A131108 A128255 A154948

Adjacent sequences: A181173 A181174 A181175 * A181177 A181178 A181179

Keyword

easy,nonn

Author

Robert G. Wilson v, Oct 08 2010

Status

approved