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

Author

Cino Hilliard, May 06 2007

Keywords

• nonn
• easy

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).

Crossrefs

Subsequence of A110673.

Programs

Magma

[30*n+23: n in [0..50]]; // Vincenzo Librandi, Feb 15 2018

Magma

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

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 *)

PARI

g(n) = forstep(x=23,n,30,print1(x","))

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)