

A128468


a(n) = 30*n + 17.


8



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
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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 = 0..1999
Index entries for linear recurrences with constant coefficients, signature (2,1).


FORMULA

From Robert Israel, Dec 10 2014: (Start)
G.f.: x*(13*x+17)/(x1)^2.
E.g.f.: 13 + (30*x13)*exp(x). (End)
a(n) = 2*a(n1)  a(n2) for n >= 2.  Jinyuan Wang, Mar 10 2020


EXAMPLE

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


MAPLE

seq(30*n+17, n=0..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



