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

Author

Davis Smith, Feb 02 2019

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

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

Primes in this sequence: A141850.

Programs

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 *)

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

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