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A128470 30*n+1 10
1, 31, 61, 91, 121, 151, 181, 211, 241, 271, 301, 331, 361, 391, 421, 451, 481, 511, 541, 571, 601, 631, 661, 691, 721, 751, 781, 811, 841, 871, 901, 931, 961, 991, 1021, 1051, 1081, 1111, 1141, 1171, 1201, 1231, 1261, 1291, 1321, 1351, 1381, 1411, 1441, 1471 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Possible upper bounds of twin primes pairs ending in 1: For a 30k+r "wheel", k > 0, r = 1, 13, 19 are the only possible values that can form an upper bound of a twin prime pair. The 30k+r wheel gives the sequence 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 subtracting 2 from 30k+7, 11, 17, 23 will gives us a multiple of 3 or 5 precludes these numbers from being an upper bound of a twin prime pair. This leaves us with r = 1, 13, 19 for k>0 as the only possible cases to form an upper bound of a twin prime pair. 1, 13, 19 concludes the 6 numbers of the 8 number wheel that can form part of a twin prime pair.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Counting Twin Primes

FORMULA

(MAGMA) [30*n+1: n in [0..50]]; // Vincenzo Librandi, // Jun 16 2011

EXAMPLE

61 = 30*2 + 1, the upper part of the twin prime pair 59,61.

MATHEMATICA

Range[1, 3000, 30] (* Vladimir Joseph Stephan Orlovsky, Jun 15 2011 *)

CROSSREFS

A161700, A005408, A016813, A016921, A017281, A017533, A158057, A161705, A161709, A161714. [From Reinhard Zumkeller, Jun 17 2009]

Sequence in context: A073650 A078562 A054804 * A195744 A132230 A136066

Adjacent sequences:  A128467 A128468 A128469 * A128471 A128472 A128473

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, May 06 2007

STATUS

approved

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Last modified October 25 17:08 EDT 2014. Contains 248557 sequences.