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A128468 a(n) = 30*n + 17. 7
17, 47, 77, 107, 137, 167, 197, 227, 257, 287, 317, 347, 377, 407, 437, 467, 497, 527, 557, 587, 617, 647, 677, 707, 737, 767, 797, 827, 857, 887, 917, 947, 977, 1007, 1037, 1067, 1097, 1127, 1157, 1187, 1217, 1247, 1277, 1307, 1337, 1367, 1397, 1427, 1457 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Previous name was: Numbers of the form 30k+17 or possible lower members of twin primes pairs ending in 7.

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 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 member of a twin prime pair.

Numbers n such that n==7 (mod 10) and n==5 (mod 6). - Vincenzo Librandi, Jun 25 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

FORMULA

G.f.: x*(13*x+17)/(x-1)^2.  E.g.f.: 13 + (30*x-13)*exp(x). - Robert Israel, Dec 10 2014

EXAMPLE

17 = 30*0 + 17, the lower part of the twin prime pair 17,19.

MAPLE

seq(30*n-13, n=1..100); # Robert Israel, Dec 10 2014

MATHEMATICA

Range[17, 7000, 30] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)

PROG

(PARI) g(n) = forstep(x=17, n, 30, print1(x", "))

CROSSREFS

Cf. A001359.

Sequence in context: A126912 A051616 A061275 * A031374 A201792 A039949

Adjacent sequences:  A128465 A128466 A128467 * A128469 A128470 A128471

KEYWORD

nonn,easy

AUTHOR

Cino Hilliard, May 05 2007

EXTENSIONS

Offset changed to 0, new name from Joerg Arndt, Dec 11 2014

STATUS

approved

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Last modified May 27 20:02 EDT 2015. Contains 257884 sequences.