A275708 a(1)=1, a(2)=2; thereafter a(n) is the smallest positive integer not yet used such that a(n)+a(n-1)-a(n-2) is a square.

1, 2, 3, 8, 4, 5, 15, 6, 10, 12, 7, 9, 14, 11, 19, 17, 18, 24, 30, 43, 23, 21, 27, 58, 33, 26, 16, 35, 45, 39, 22, 42, 29, 38, 40, 34, 31, 28, 52, 25, 36, 53, 32, 37, 20, 66, 54, 13, 50, 44, 55, 70, 49, 46, 67

Offset: 1

Author

Zak Seidov, Aug 06 2016

Keywords

• nonn

Comments

Apparently this is a permutation of positive numbers. Out of the first 10000 terms the missing numbers are:

8974, 9298, 9342, 9380, 9386, 9425, 9429, 9454, 9495, 9497, 9525,...,

while the maximal term is a(9919)=10802.

Corresponding squares:

4, 9, 9, 1, 16, 16, 1, 16, 9, 4, 16, 16, 16, 25, 16, 25, 36, 49, 36, 1, 25, 64, 64, 1, ...

Examples

			-1+2+3=4, -2+3+8=9, -3+8+4=9.
		

Crossrefs

Cf. A076991.

Programs

Mathematica

s={1,2};Do[a = s[[-1]] - s[[-2]]; k = 1; While[(b=k^2-a)<=0 || MemberQ[s,b], k++]; AppendTo[s, k^2 - a], {100}]; s