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A164097
Numbers k such that 6*k + 7 is a perfect square.
3
3, 7, 19, 27, 47, 59, 87, 103, 139, 159, 203, 227, 279, 307, 367, 399, 467, 503, 579, 619, 703, 747, 839, 887, 987, 1039, 1147, 1203, 1319, 1379, 1503, 1567, 1699, 1767, 1907, 1979, 2127, 2203, 2359, 2439, 2603, 2687, 2859, 2947, 3127, 3219, 3407, 3503, 3699
OFFSET
1,1
COMMENTS
The entries are prime, or divisible by 3, or divisible by prime of the form 3*m+1.
FORMULA
From R. J. Mathar, Aug 26 2009: (Start)
a(n) = a(n-1) +2*a(n-2) -2*a(n-3) -a(n-4) +a(n-5).
G.f.: x*(-3-4*x-6*x^2+x^4)/((1+x)^2*(x-1)^3).
a(n) = 3*(2*n-1+2*n^2)/4 -(-1)^n*(1+2*n)/4 = A062717(n+1)-1. (End)
Sum_{n>=1} 1/a(n) = 1 + (tan((2+sqrt(7))*Pi/6) - cot((1+sqrt(7))*Pi/6))*Pi/(2*sqrt(7)). - Amiram Eldar, Feb 24 2023
MATHEMATICA
Select[Range[4000], IntegerQ[Sqrt[6 # + 7 ]] &] (* or *) LinearRecurrence[{1, 2, -2, -1, 1}, {3, 7, 19, 27, 47}, 50] (* Harvey P. Dale, Apr 29 2011 *)
PROG
(Magma) [n: n in [1..4000] | IsSquare(6*n+7)]; // Vincenzo Librandi, Oct 12 2012
CROSSREFS
Cf. A062717, A104777 (the squares 6*k+7).
Sequence in context: A203321 A203319 A366171 * A171140 A186452 A016046
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Aug 10 2009
EXTENSIONS
Edited by R. J. Mathar, Aug 26 2009
STATUS
approved