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A128469 Numbers of the form 30k+29 or possible lower bounds of twin primes pairs ending in 9. 1


%S 29,59,89,119,149,179,209,239,269,299,329,359,389,419,449,479,509,539,

%T 569,599,629,659,689,719,749,779,809,839,869,899,929,959,989,1019,

%U 1049,1079,1109,1139,1169,1199,1229,1259,1289,1319,1349,1379,1409,1439,1469

%N Numbers of the form 30k+29 or possible lower bounds of twin primes pairs ending in 9.

%C 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.

%C Of the first 10000 terms of this sequence, only 988 are lower primes of a twin prime pair. [_Harvey P. Dale_, May 05 2011]

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

%t 30Range[0,60]+29 (* _Harvey P. Dale_, May 05 2011 *)

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

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, May 05 2007

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Last modified April 10 10:39 EDT 2021. Contains 342845 sequences. (Running on oeis4.)