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

1,1

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.

Links

Table of n, a(n) for n=1..55.

Formula

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

Example

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

Crossrefs

Cf. A001844, A004431, A055096, A270835.

Sequence in context: A278252 A274298 A270835 * A152678 A110758 A189765

Adjacent sequences: A272060 A272061 A272062 * A272064 A272065 A272066

Keyword

nonn

Author

Bob Selcoe, Apr 19 2016

Status

approved