A226076 Lexicographically least sequence of squares that are sum-free.

1, 4, 9, 16, 36, 64, 144, 256, 289, 576, 1024, 1156, 2304, 4096, 4624, 9216, 16384, 18496, 36864, 65536, 73984, 147456, 262144, 295936, 589824, 1048576, 1183744, 2359296, 4194304, 4734976, 9437184, 16777216, 18939904, 37748736, 67108864, 75759616, 150994944

Offset: 1

Author

Frank M Jackson, May 25 2013

Keywords

• nonn

Comments

A sum-free sequence has no term that is the sum of a subset of its previous terms. There are an infinite number of sequences that are subsets of the squares and sum-free. This sequence is lexicographically the first.

Examples

			a(10)=576 as 576 is the next square after a(9)=289 that cannot be formed from distinct sums of a(1),...,a(9) (1,4,9,16,36,64,144,256,289).
		

Links

• H. L. Abbott, On sum-free sequences
• Eric W. Weisstein, MathWorld: A-Sequence
• Wikipedia, Sum-free sequence

Crossrefs

Cf. A225947.

Programs

Mathematica

memberQ[n1_, k1_] := If[Select[IntegerPartitions[n1^2, Length[k1], k1], Sort@#==Union@# &]=={}, False, True]; k={1}; n=1; While[Length[k]<20, (If[!memberQ[n, k], k=Append[k, n^2]]; n++)]; k

Formula

Conjecture: a(n) = 4*a(n-3) for n>9. G.f.: -x*(33*x^8 +112*x^7 +80*x^6 +28*x^5 +20*x^4 +12*x^3 +9*x^2 +4*x +1) / (4*x^3 -1). - Colin Barker, May 28 2013

Extensions

More terms from Colin Barker, May 28 2013

a(33)-a(37) from Donovan Johnson, Dec 17 2013