A263920 A positive integer n is in this sequence iff arctan(n)^2 can be represented as Sum_{0

7, 47, 57, 99, 117

Offset: 1

Author

Vladimir Reshetnikov, Oct 29 2015

Keywords

• nonn
• hard
• more

Comments

The terms given are certainly in the sequence. Although I lack a rigorous proof that no intermediate terms were omitted, an extensive computer search gave no other candidates in between.

It is an open question if the sequence is infinite.

Examples

			7 is in the sequence, because arctan(7)^2 = -5*arctan(1)^2 + (10/3)*arctan(2)^2 + (2/3)*arctan(3)^2.
47 is in the sequence, because arctan(47)^2 = (2939/210)*arctan(2)^2 - (125/21)*arctan(3)^2 - (6/5)*arctan(4)^2 - (12/7)*arctan(5)^2 - (29/7)*arctan(7)^2 + (15/7)*arctan(8)^2 + (2/5)*arctan(13)^2 + (11/7)*arctan(18)^2 - arctan(21)^2 + (7/10)*arctan(38)^2.
		

Links

• Eric Weisstein's MathWorld, Inverse Tangent.

Crossrefs

Cf. A005528, A002312.