A248474 Numbers congruent to 13 or 17 mod 30.

13, 17, 43, 47, 73, 77, 103, 107, 133, 137, 163, 167, 193, 197, 223, 227, 253, 257, 283, 287, 313, 317, 343, 347, 373, 377, 403, 407, 433, 437, 463, 467, 493, 497, 523, 527, 553, 557, 583, 587, 613, 617

Offset

1,1

Comments

The combination of A082369(30*n+13) and A128468(30*n+17) is the base sequence for A140533(Primes congruent to 13 or 17 mod 30).

Links

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000

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

Formula

From Colin Barker, Oct 07 2014: (Start)

a(n) = (-15-11*(-1)^n+30*n)/2.

a(n) = a(n-1)+a(n-2)-a(n-3).

G.f.: x*(13*x^2+4*x+13) / ((x-1)^2*(x+1)).

(End)

E.g.f.: 13 + ((30*x - 15)*exp(x) - 11*exp(-x))/2. - David Lovler, Sep 10 2022

Mathematica

Flatten[Table[{15n - 2, 15n + 2}, {n, 1, 41, 2}]] (* Alonso del Arte, Oct 06 2014 *)

Prog

(Python)
for n in range(1, 101):
..print (n*30-17),
..print (n*30-13),
(PARI)
Vec(x*(13*x^2+4*x+13)/((x-1)^2*(x+1)) + O(x^100)) \\ Colin Barker, Oct 07 2014

Crossrefs

Cf. A082369 (30*n+13), A128468 (30*n+17).

Cf. A039949 (Primes of the form 30n-13), A132233 (Primes congruent to 13 mod 30), A140533 (Primes congruent to 13 or 17 mod 30).

Sequence in context: A068497 A125524 A156553 * A140533 A180527 A076789

Adjacent sequences: A248471 A248472 A248473 * A248475 A248476 A248477

Keyword

nonn,easy

Author

Karl V. Keller, Jr., Oct 06 2014

Status

approved