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A263920
A positive integer n is in this sequence iff arctan(n)^2 can be represented as Sum_{0<k<n} c(k)*arctan(k)^2 with rational c(k). The terms are in increasing order.
0
7, 47, 57, 99, 117
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
Sequence in context: A089725 A086040 A009241 * A124837 A122731 A059452
KEYWORD
nonn,hard,more
AUTHOR
STATUS
approved