A272063 a(n) = largest k such that A004431(n) +/- k are both positive squares.

4, 6, 12, 8, 16, 24, 10, 20, 30, 12, 24, 40, 36, 14, 48, 28, 42, 60, 56, 32, 48, 70, 64, 18, 84, 80, 54, 72, 96, 20, 40, 90, 60, 112, 80, 108, 22, 100, 126, 120, 88, 144, 110, 48, 140, 72, 132, 96, 160, 120, 154, 52, 78, 144, 180

Offset: 1

Author

Bob Selcoe, Apr 19 2016

Keywords

• nonn

Comments

There can be more than one value of k such that A004431(n) +/- k are both positive squares; i.e., when there are multiple ways to express A004431(n) as the sum of positive squares. These are the terms which appear more than once in A055096. For example A004431(19) = 65 = {(1^2 + 8^2), (4^2 + 7^2)}: 65 +/- 16 = {7^2, 9^2} and 65 +/- 56 = {3^2, 11^2}. So a(19) = 56 rather than 16.

Similar to A270835; differences occur for n<56 at n = {19,25,38,39,42,51}; i.e., terms A004431(n) which appear more than once in A055096.

Sequence contains every even number >=4 and no odd numbers.

Examples

			a(11)=24 because A004431(11) = 40; 40+24 = 8^2 and 40-24 = 4^2.
		

Crossrefs

Cf. A001844, A004431, A055096, A270835.

Formula

a(n) = A004431(n)-1 when A004431(n) = k^2 + (k+1)^2 == A001844(k), k>=1.