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A269819
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Numbers that are congruent to {5, 11, 13, 19} mod 24.
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3
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5, 11, 13, 19, 29, 35, 37, 43, 53, 59, 61, 67, 77, 83, 85, 91, 101, 107, 109, 115, 125, 131, 133, 139, 149, 155, 157, 163, 173, 179, 181, 187, 197, 203, 205, 211, 221, 227, 229, 235, 245, 251, 253, 259, 269, 275, 277, 283, 293, 299, 301, 307, 317
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OFFSET
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1,1
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COMMENTS
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No terms are multiples of 3.
Numbers such that (j+5)*(j-5)/48 are positive integers. Equivalent to positive integers (m+3)*(m-2)/12, with m == {2,5,6,9} mod 12 (observation made in A268539 by M. F. Hasler, Mar 02 2016).
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LINKS
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FORMULA
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a(n) = a(n-4) + 24.
G.f.: x*(1+x)*(5-4*x+5*x^2) / ((1-x)^2*(1+x^2)). - Colin Barker, Mar 06 2016
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.
a(n) = 6*n-3-(1-i)*i^(-n)-(1+i)*i^n for i=sqrt(-1). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (2-sqrt(2))*Pi/12. - Amiram Eldar, Dec 31 2021
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MAPLE
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MATHEMATICA
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Table[24 n + {5, 11, 13, 19}, {n, 0, 12}] // Flatten (* Michael De Vlieger, Mar 07 2016 *)
LinearRecurrence[{2, -2, 2, -1}, {5, 11, 13, 19}, 60] (* Harvey P. Dale, Nov 17 2017 *)
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PROG
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(Magma) I:=[5, 11, 13, 19]; [n le 4 select I[n] else Self(n-4) + 24 : n in [1..60]]; // Vincenzo Librandi, Mar 06 2016
(PARI) Vec(x*(1+x)*(5-4*x+5*x^2)/((1-x)^2*(1+x^2)) + O(x^100)) \\ Colin Barker, Mar 06 2016
(Magma) [n : n in [0..400] | n mod 24 in [5, 11, 13, 19]]; // Wesley Ivan Hurt, Jun 04 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Incorrect term 252 replaced by two missing terms 251 and 253 by Colin Barker, Mar 06 2016
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STATUS
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approved
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