A269819 Numbers that are congruent to {5, 11, 13, 19} mod 24.

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

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

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

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

Adjacent sequences: A269816 A269817 A269818 * A269820 A269821 A269822

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