



2, 3, 13, 19, 31, 43, 53, 61, 71, 73, 101, 103, 109, 113, 131, 139, 151, 157, 173, 181, 191, 193, 199, 229, 233, 239, 241, 251, 269, 271, 283, 293, 311, 313, 349, 353, 373, 379, 409, 419, 421, 433, 439, 443, 463, 491, 499, 509, 523, 571, 577, 593, 599, 601
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OFFSET

1,1


COMMENTS

Every greater of twin primes (A006512), beginning with 13, is in the sequence.
A very simple sieve for the generation of the terms is the following: Let p_n be the nth prime. Consider consecutive intervals of the form (2p_n, 2p_{n+1}), n=1,2,... From every interval containing at least one prime we take the first one and remove it from the set of all primes. Then all remaining primes form the sequence. Let us demonstrate this sieve: For primes 2,3,5,7,11,... consider intervals (4,6), (6,10), (10,14), (14,22), (22,26), (26,34), ... . Removing from the set of all primes the first prime of each interval, i.e., 5,7,11,17,23,29,... ,we obtain 2,3,13,19,31, etc.
This sequence and A164368 are the mutually wrapping up sequences:
Following the steps to generate T(n,1) in A229608 provides an alternate method of generating this sequence.  Bob Selcoe, Oct 27 2015


LINKS



FORMULA



MATHEMATICA

primePiMax = 200;
Join[{2, 3}, Select[Table[{(Prime[k1] + 1)/2, (Prime[k]  1)/2}, {k, 3, primePiMax}], AllTrue[Range[#[[1]], #[[2]]], CompositeQ]&][[All, 2]]*2+1] (* JeanFrançois Alcover, Aug 18 2018 *)


CROSSREFS

If the first two terms are omitted we get A164333.


KEYWORD

nonn


AUTHOR



STATUS

approved



