A128471 a(n) = 30*n + 7.

7, 37, 67, 97, 127, 157, 187, 217, 247, 277, 307, 337, 367, 397, 427, 457, 487, 517, 547, 577, 607, 637, 667, 697, 727, 757, 787, 817, 847, 877, 907, 937, 967, 997, 1027, 1057, 1087, 1117, 1147, 1177, 1207, 1237, 1267, 1297, 1327, 1357, 1387, 1417, 1447, 1477

Offset: 0

Author

Cino Hilliard, May 06 2007

Keywords

• easy
• nonn

Comments

30*n + 7 -/+ 2 is a multiple of 3 or 5. For n > 0, this number is not prime. So with the exception of a(0), no a(n) is a member of a twin prime pair.

Except for 7, these numbers cannot be written as sum or difference of two primes. - Arkadiusz Wesolowski, Jan 08 2012

Links

• Albert van der Horst, Counting Twin Primes.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Programs

Mathematica

Range[7,7000,30] (* Vladimir Joseph Stephan Orlovsky, Jun 18 2011 *)
LinearRecurrence[{2,-1},{7,37},50] (* Harvey P. Dale, Jul 31 2024 *)

PARI

A128471(n)={ return(30*n+7) ; }
for(n=0,30,print1(A128471(n)",")) ; /* R. J. Mathar, Sep 05 2010 */

Formula

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Sep 05 2010

G.f.: (7+23*x)/(1-x)^2. - R. J. Mathar, Sep 05 2010

E.g.f.: exp(x)*(7 + 30*x). - Elmo R. Oliveira, Apr 04 2025

Extensions

Comment clarified by Robert Israel, offset set to zero by R. J. Mathar, Sep 05 2010