A128467 a(n) = 30*n + 11.

11, 41, 71, 101, 131, 161, 191, 221, 251, 281, 311, 341, 371, 401, 431, 461, 491, 521, 551, 581, 611, 641, 671, 701, 731, 761, 791, 821, 851, 881, 911, 941, 971, 1001, 1031, 1061, 1091, 1121, 1151, 1181, 1211, 1241, 1271, 1301, 1331, 1361, 1391, 1421, 1451

Offset: 0

Author

Cino Hilliard, May 05 2007

Keywords

• easy
• nonn

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.

Examples

			41 = 30*1 + 11, the lower part of the twin prime pair 41,43.
		

Programs

Mathematica

Range[11, 7000, 30] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
30*Range[0,50]+11 (* Harvey P. Dale, Oct 09 2023 *)

PARI

forstep(x=11,1500,30,print1(x","))

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)

Extensions

Offset corrected by Eric Rowland, Aug 15 2017