OFFSET
0,1
COMMENTS
x^2 + 30 != y^n for all x,y and n > 1, so this is a subsequence of A007916.
From Bruno Berselli, May 12 2014: (Start)
This is the case k=5 of the identity n^2 + k*(k+1) = ( Sum_{i=-k..k} (n+i)^3 ) / ( (2*k+1)*n ).
The old name of this sequence was: Numbers of the form x^2 + 30. Also numbers that are not a perfect power.
LINKS
Shawn A. Broyles, Table of n, a(n) for n = 0..1000
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 04 2020: (Start)
Sum_{n>=0} 1/a(n) = (1 + sqrt(30)*Pi*coth(sqrt(30)*Pi))/60.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(30)*Pi*cosech(sqrt(30)*Pi))/60. (End)
EXAMPLE
11*4*a(4) = (-1)^3 + 0^3 + 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 8^3 + 9^3 = 2024. - Bruno Berselli, May 12 2014
MATHEMATICA
Range[0, 60]^2+30 (* Harvey P. Dale, Oct 17 2022 *)
PROG
(PARI) g(n, p) = for(x=0, n, y=x^2+p; print1(y", "));
(PARI) a(n) = n^2 + 30; \\ Altug Alkan, Apr 30 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Cino Hilliard, Feb 21 2006
EXTENSIONS
New name from Shawn A. Broyles and Altug Alkan, Apr 30 2018
STATUS
approved