A128473 Numbers of the form 30*k+23 or numbers that cannot be part of a twin prime pair.

23, 53, 83, 113, 143, 173, 203, 233, 263, 293, 323, 353, 383, 413, 443, 473, 503, 533, 563, 593, 623, 653, 683, 713, 743, 773, 803, 833, 863, 893, 923, 953, 983, 1013, 1043, 1073, 1103, 1133, 1163, 1193, 1223, 1253, 1283, 1313, 1343, 1373, 1403, 1433, 1463

Offset

1,1

Comments

30*k + 23 -+ 2 is a multiple of 3 or 5 precluding it from being part of a twin prime pair.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Albert van der Horst, Counting Twin Primes

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

From Vincenzo Librandi, Feb 15 2018: (Start)

G.f.: x*(23 + 7*x)/(1 - x)^2.

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

Mathematica

Range[23, 7000, 30] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
CoefficientList[Series[(23 + 7 x) / (1 - x)^2, {x, 0, 50}], x] (* Vincenzo Librandi, Feb 15 2018 *)
LinearRecurrence[{3, -3, 1}, {23, 53, 83}, 50] (* or *) NestList[#+30&, 23, 50] (* Harvey P. Dale, Sep 11 2019 *)

Prog

(PARI) g(n) = forstep(x=23, n, 30, print1(x", "))
(Magma) [30*n+23: n in [0..50]] /* or */ I:=[23, 53, 83]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 15 2018

Crossrefs

Subsequence of A110673.

Sequence in context: A055782 A338821 A104802 * A132235 A277993 A339188

Adjacent sequences: A128470 A128471 A128472 * A128474 A128475 A128476

Keyword

nonn,easy

Author

Cino Hilliard, May 06 2007

Status

approved