A130108 Rearrangement of natural numbers such that each three terms sum up to a perfect square.

1, 2, 6, 3, 4, 9, 5, 7, 13, 8, 10, 18, 11, 12, 26, 14, 15, 20, 16, 17, 31, 19, 21, 24, 22, 23, 36, 25, 27, 29, 28, 30, 42, 32, 33, 35, 34, 37, 50, 38, 39, 44, 40, 41, 63, 43, 45, 56, 46, 47, 51, 48, 49, 72, 52, 53, 64, 54, 55, 60, 57, 58, 81, 59, 61, 76, 62, 65, 69, 66, 67, 92

Offset

1,2

Comments

s={1,2,6}, 1+2+6=9=3^2. Then select the least three numbers a<b<c, such that all a, b, c are absent in s and a+b+c=d^2, a perfect square. Join s and {a,b,c}, repeat procedure. Numbers r which retain their position (that is, s[[r]]=r): 1,2,24,51,60,69,102,168,216,393,882. Also, no finite subset of length t is a permutation of {1..t}.

Links

Table of n, a(n) for n=1..72.

Example

1+2+6=9, 3+4+9=16, 5+7+13=25, 8+10+18=36, 11+12+26=49,14+15+20=49.

Mathematica

s={}; ra=Range[2000]; Do[su=ra[[1]]+ra[[2]]; c=3; While[ !IntegerQ[Sqrt[su+ra[[c]]]], c++ ]; rac=ra[[c]]; s=Join[s, {ra[[1]], ra[[2]], rac}]; ra=Complement[ra, {ra[[1]], ra[[2]], rac}], {334}]; s

Crossrefs

Cf. A130109, A130110, A130111.

Sequence in context: A262943 A357735 A163892 * A201746 A362552 A353732

Adjacent sequences: A130105 A130106 A130107 * A130109 A130110 A130111

Keyword

nonn

Author

Zak Seidov, May 08 2007

Status

approved