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

0,1

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.

Links

Table of n, a(n) for n=0..48.

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

Sequence in context: A179446 A260269 A109982 * A238713 A132232 A331555

Adjacent sequences: A128464 A128465 A128466 * A128468 A128469 A128470

Keyword

easy,nonn

Author

Cino Hilliard, May 05 2007

Extensions

Offset corrected by Eric Rowland, Aug 15 2017

Status

approved