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A219394
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Numbers k such that 17*k+1 is a square.
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3
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0, 15, 19, 64, 72, 147, 159, 264, 280, 415, 435, 600, 624, 819, 847, 1072, 1104, 1359, 1395, 1680, 1720, 2035, 2079, 2424, 2472, 2847, 2899, 3304, 3360, 3795, 3855, 4320, 4384, 4879, 4947, 5472, 5544, 6099, 6175, 6760, 6840, 7455, 7539, 8184, 8272, 8947
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OFFSET
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1,2
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COMMENTS
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Equivalently, numbers of the form m*(17*m+2), where m = 0,-1,1,-2,2,-3,3,...
Also, integer values of h*(h+2)/17.
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LINKS
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FORMULA
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G.f.: x^2*(15+4*x+15*x^2)/((1+x)^2*(1-x)^3).
a(n) = a(-n+1) = (34*n*(n-1)+13*(-1)^n*(2*n-1)+5)/8 + 1.
Sum_{n>=2} 1/a(n) = 17/4 - cot(2*Pi/17)*Pi/2. - Amiram Eldar, Mar 15 2022
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MAPLE
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local n;
for n from 1 to q do if type(sqrt(17*n+1), integer) then print(n);
fi; od; end:
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MATHEMATICA
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Select[Range[0, 9000], IntegerQ[Sqrt[17 # + 1]] &]
CoefficientList[Series[x (15 + 4 x + 15 x^2)/((1 + x)^2 (1 - x)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 18 2013 *)
LinearRecurrence[{1, 2, -2, -1, 1}, {0, 15, 19, 64, 72}, 50] (* Harvey P. Dale, May 01 2017 *)
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PROG
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(Magma) [n: n in [0..9000] | IsSquare(17*n+1)];
(Magma) I:=[0, 15, 19, 64, 72]; [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
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CROSSREFS
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Cf. similar sequences listed in A219257.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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