OFFSET
0,1
COMMENTS
Possible lower bounds of twin primes pairs ending in 1.
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 give 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 bound of a twin prime pair.
FORMULA
From R. J. Mathar, Dec 05 2007: (Start)
O.g.f.: (11+19*x)/(-1+x)^2 = 19/(-1+x) + 30/(-1+x)^2.
a(n) = 30*n + 11. (End)
EXAMPLE
41 = 30*1 + 11, the lower part of the twin prime pair 41,43.
MATHEMATICA
Range[11, 7000, 30] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
30*Range[0, 50]+11 (* Harvey P. Dale, Oct 09 2023 *)
PROG
(PARI) forstep(x=11, 1500, 30, print1(x", "))
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, May 05 2007
EXTENSIONS
Offset corrected by Eric Rowland, Aug 15 2017
STATUS
approved