OFFSET
1,1
COMMENTS
Conjecture: n^2 + 10 != x^k for all n,x, and k>1.
The conjecture is true: See Cohn. - James Rayman, Feb 14 2023
LINKS
J. H. E. Cohn, The diophantine equation x^2 + C = y^n, Acta Arithmetica LXV.4 (1993).
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Amiram Eldar, Nov 02 2020: (Start)
Sum_{n>=0} 1/a(n) = (1 + sqrt(10)*Pi*coth(sqrt(10)*Pi))/20.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(10)*Pi*cosech(sqrt(10)*Pi))/20. (End)
From Amiram Eldar, Feb 12 2024: (Start)
Product_{n>=0} (1 - 1/a(n)) = (3/sqrt(10))*sinh(3*Pi)/sinh(sqrt(10)*Pi).
Product_{n>=0} (1 + 1/a(n)) = sqrt(11/10)*sinh(sqrt(11)*Pi)/sinh(sqrt(10)*Pi). (End)
MATHEMATICA
a[n_]:=n^2+10; a[Range[200]] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2011*)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Feb 21 2006
EXTENSIONS
Edited by Charles R Greathouse IV, Aug 09 2010
STATUS
approved