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A248474
Numbers congruent to 13 or 17 mod 30.
1
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, 643, 647, 673, 677, 703, 707, 733, 737, 763, 767, 793, 797
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).
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
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2*(5+sqrt(5)))+sqrt(3)-sqrt(15))*Pi / (30*(sqrt(6*(5+sqrt(5)))+sqrt(5)-1)). - Amiram Eldar, Jul 30 2024
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
KEYWORD
nonn,easy
AUTHOR
Karl V. Keller, Jr., Oct 06 2014
STATUS
approved