

A130108


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


3



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
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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: A236557 A262943 A163892 * A201746 A026203 A317025
Adjacent sequences: A130105 A130106 A130107 * A130109 A130110 A130111


KEYWORD

nonn


AUTHOR

Zak Seidov, May 08 2007


STATUS

approved



