OFFSET
0,1
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
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1999
Index entries for linear recurrences with constant coefficients, signature (2,-1).
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
EXAMPLE
17 = 30*0 + 17, the lower part of the twin prime pair 17,19.
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 *)
PROG
(PARI) g(n) = forstep(x=17, n, 30, print1(x", "))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Cino Hilliard, May 05 2007
EXTENSIONS
Offset changed to 0, new name from Joerg Arndt, Dec 11 2014
STATUS
approved