A128468 a(n) = 30*n + 17.

17, 47, 77, 107, 137, 167, 197, 227, 257, 287, 317, 347, 377, 407, 437, 467, 497, 527, 557, 587, 617, 647, 677, 707, 737, 767, 797, 827, 857, 887, 917, 947, 977, 1007, 1037, 1067, 1097, 1127, 1157, 1187, 1217, 1247, 1277, 1307, 1337, 1367, 1397, 1427, 1457

Offset: 0

Author

Cino Hilliard, May 05 2007

Keywords

• nonn
• easy

Comments

Previous name was: Numbers of the form 30k+17 or possible lower members of twin primes pairs ending in 7.

For a 30k+r "wheel", r = 11,17,29 are the only possible values that can form a lower twin prime pair. The 30k+r wheel gives the recurrence 1, 7,11,13,17,19,23,29 31,37,41,43,47,49,53,59 .. which is frequently used in prime number sieves to skip multiples of 2,3,5. The fact that adding 2 to 30k+1,7,13,19,23 will gives us a multiple of 3 or 5, precludes these numbers from being a lower member of a twin prime pair. This leaves us with r = 11,17,29 as the only possible cases to form a lower member of a twin prime pair.

Numbers n such that n==7 (mod 10) and n==5 (mod 6). - Vincenzo Librandi, Jun 25 2014

Examples

			17 = 30*0 + 17, the lower part of the twin prime pair 17,19.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1999
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A001359.

Programs

Maple

seq(30*n+17, n=0..100); # Robert Israel, Dec 10 2014

Mathematica

Range[17, 7000, 30] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)

PARI

g(n) = forstep(x=17,n,30,print1(x","))

Formula

From Robert Israel, Dec 10 2014: (Start)

G.f.: x*(13*x+17)/(x-1)^2.

E.g.f.: 13 + (30*x-13)*exp(x). (End)

a(n) = 2*a(n-1) - a(n-2) for n >= 2. - Jinyuan Wang, Mar 10 2020

Extensions

Offset changed to 0, new name from Joerg Arndt, Dec 11 2014