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A219389 Numbers k such that 13*k+1 is a square. 3
0, 11, 15, 48, 56, 111, 123, 200, 216, 315, 335, 456, 480, 623, 651, 816, 848, 1035, 1071, 1280, 1320, 1551, 1595, 1848, 1896, 2171, 2223, 2520, 2576, 2895, 2955, 3296, 3360, 3723, 3791, 4176, 4248, 4655, 4731, 5160, 5240, 5691, 5775, 6248, 6336, 6831, 6923 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Equivalently, numbers of the form m*(13*m+2), where m = 0,-1,1,-2,2,-3,3,...
Also, integer values of h*(h+2)/13.
LINKS
FORMULA
G.f.: x^2*(11+4*x+11*x^2)/((1+x)^2*(1-x)^3).
a(n) = a(-n+1) = (26*n*(n-1)+9*(-1)^n*(2*n-1)+1)/8 +1.
Sum_{n>=2} 1/a(n) = 13/4 - cot(2*Pi/13)*Pi/2. - Amiram Eldar, Mar 15 2022
MAPLE
A219389:=proc(q)
local n;
for n from 1 to q do if type(sqrt(13*n+1), integer) then print(n);
fi; od; end:
A219389(1000); # Paolo P. Lava, Feb 19 2013
MATHEMATICA
Select[Range[0, 7000], IntegerQ[Sqrt[13 # + 1]] &]
CoefficientList[Series[x (11 + 4 x + 11 x^2)/((1 + x)^2 (1 - x)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 18 2013 *)
PROG
(Magma) [n: n in [0..7000] | IsSquare(13*n+1)];
(Magma) I:=[0, 11, 15, 48, 56]; [n le 5 select I[n] else Self(n-1)+2*Self(n-2)-2*Self(n-3)-Self(n-4)+Self(n-5): n in [1..50]]; // Vincenzo Librandi, Aug 18 2013
CROSSREFS
Cf. similar sequences listed in A219257.
Cf. A175886 (square roots of 13*a(n)+1).
Sequence in context: A068483 A357626 A241679 * A217085 A267123 A115779
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Nov 19 2012
STATUS
approved

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)