OFFSET
1,1
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.
LINKS
Eric Weisstein's MathWorld, Inverse Tangent.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Vladimir Reshetnikov, Oct 29 2015
STATUS
approved