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A269819 Numbers that are congruent to {5, 11, 13, 19} mod 24. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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).
LINKS
FORMULA
a(n) = a(n-4) + 24.
a(n) = sqrt(48*A268539(n) + 25).
G.f.: x*(1+x)*(5-4*x+5*x^2) / ((1-x)^2*(1+x^2)). - Colin Barker, Mar 06 2016
From Wesley Ivan Hurt, Jun 04 2016: (Start)
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
MAPLE
A269819:=n->6*n-3-(1-I)*I^(-n)-(1+I)*I^n: seq(A269819(n), n=1..80); # Wesley Ivan Hurt, Jun 04 2016
MATHEMATICA
Table[24 n + {5, 11, 13, 19}, {n, 0, 12}] // Flatten (* Michael De Vlieger, Mar 07 2016 *)
Table[6n-3-(1-I)*I^(-n)-(1+I)*I^n, {n, 80}] (* Wesley Ivan Hurt, Jun 04 2016 *)
LinearRecurrence[{2, -2, 2, -1}, {5, 11, 13, 19}, 60] (* Harvey P. Dale, Nov 17 2017 *)
PROG
(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
CROSSREFS
Subsequence of A001651.
Cf. A268539.
Sequence in context: A292940 A098085 A104216 * A040144 A019395 A045448
KEYWORD
nonn,easy
AUTHOR
Bob Selcoe, Mar 05 2016
EXTENSIONS
Incorrect term 252 replaced by two missing terms 251 and 253 by Colin Barker, Mar 06 2016
STATUS
approved

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)