A306279 Numbers congruent to 3 or 18 mod 22.

3, 18, 25, 40, 47, 62, 69, 84, 91, 106, 113, 128, 135, 150, 157, 172, 179, 194, 201, 216, 223, 238, 245, 260, 267, 282, 289, 304, 311, 326, 333, 348, 355, 370, 377, 392, 399, 414, 421, 436, 443, 458, 465, 480, 487, 502, 509, 524, 531, 546, 553, 568

Offset

1,1

Links

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

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

Formula

a(n) = 11*n - 6 + 2*(-1)^n.

a(n) = 11*n - A105398(n + 4).

A007310(a(n) + 1) = 11*A007310(n).

From Colin Barker, Feb 07 2019: (Start)

G.f.: x*(3 + 15*x + 4*x^2) / ((1 - x)^2*(1 + x)).

a(n) = a(n - 1) + a(n - 2) - a(n - 3) for n > 3. (End)

E.g.f.: 4 + (11*x - 6)*exp(x) + 2*exp(-x). - David Lovler, Sep 08 2022

Maple

seq(seq(22*i+j, j=[3, 18]), i=0..200);

Mathematica

Select[Range[200], MemberQ[{3, 18}, Mod[#, 22]] &]
Flatten[Table[{22n + 3, 22n + 18}, {n, 0, 43}]] (* Alonso del Arte, Feb 18 2019 *)

Prog

(PARI) for(n=3, 678, if((n%22==3) || (n%22==18), print1(n, ", ")))
(PARI) vector(62, n, 11*n-6+2*(-1)^n)
(PARI) Vec(x*(3 + 15*x + 4*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ Colin Barker, Feb 07 2019
(Scala) (3 to 949 by 22).union(18 to 942 by 22).sorted // Alonso del Arte, Feb 18 2019

Crossrefs

Cf. A007310, A020639, A042948, A091999, A105398, A131555, A141850, A158459, A273669, A306277, A306289.

Primes in this sequence: A141850.

Sequence in context: A346421 A263578 A048080 * A169598 A202359 A118474

Adjacent sequences: A306276 A306277 A306278 * A306280 A306281 A306282

Keyword

nonn,easy

Author

Davis Smith, Feb 02 2019

Status

approved