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A128469 Numbers of the form 30k+29 or possible lower bounds of twin primes pairs ending in 9. 1
29, 59, 89, 119, 149, 179, 209, 239, 269, 299, 329, 359, 389, 419, 449, 479, 509, 539, 569, 599, 629, 659, 689, 719, 749, 779, 809, 839, 869, 899, 929, 959, 989, 1019, 1049, 1079, 1109, 1139, 1169, 1199, 1229, 1259, 1289, 1319, 1349, 1379, 1409, 1439, 1469 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For a 30k+r "wheel", r = 11,17,29 are the only possible values that can form a 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 bound of a twin prime pair. The lower bound of twin prime pairs can only end in 1,7 or 9 since adding 2 to primes ending in 3 become multiples of 5.

Of the first 10000 terms of this sequence, only 988 are lower primes of a twin prime pair. [From Harvey P. Dale, May 05 2011]

LINKS

Table of n, a(n) for n=1..49.

EXAMPLE

59 = 30*1 + 29, the lower part of the twin prime pair 59,61.

MATHEMATICA

30Range[0, 60]+29 (* Harvey P. Dale, May 05 2011 *)

PROG

(PARI) g(n) = forstep(x=29, n, 30, print1(x", "))

CROSSREFS

Sequence in context: A042668 A042664 A042662 * A132236 A158477 A161928

Adjacent sequences:  A128466 A128467 A128468 * A128470 A128471 A128472

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, May 05 2007

STATUS

approved

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Last modified December 10 03:42 EST 2016. Contains 278993 sequences.