A166252 - OEIS

%I #19 Jun 01 2023 22:32:40

%S 71,101,109,151,181,191,229,233,239,241,269,283,311,349,373,409,419,

%T 433,439,491,571,593,599,601,607,643,647,653,659,683,727,823,827,857,

%U 941,947,991,1021,1031,1033,1051,1061,1063,1091,1103,1301,1373,1427,1429

%N Primes which are not the smallest or largest prime in an interval of the form (2*prime(k),2*prime(k+1)).

%C Called "central primes" in A166251, not to be confused with the central polygonal primes A055469.

%C The primes tabulated in intervals (2*prime(k),2*prime(k+1)) are

%C 5, k=1

%C 7, k=2

%C 11,13, k=3

%C 17,19, k=4

%C 23,    k=5

%C 29,31, k=6

%C 37,    k=7

%C 41,43, k=8

%C 47,53, k=9

%C 59,61, k=10

%C 67,71,73,  k=11

%C 79,        k=12

%C 83,     k=13

%C 89,     k=14

%C 97,101,103, k=15

%C and only rows with at least 3 primes contribute primes to the current sequence.

%C For n >= 2, these are numbers of A164368 which are in A194598. - Vladimir Shevelev, Apr 27 2012

%H T. D. Noe, <a href="/A166252/b166252.txt">Table of n, a(n) for n = 1..1000</a>

%e Since 2*31 < 71 < 2*37 and the interval (62, 74) contains prime 67 < 71 and prime 73 > 71, then 71 is in the sequence.

%t n = 0; t = {}; While[Length[t] < 100, n++; ps = Select[Range[2*Prime[n], 2*Prime[n+1]], PrimeQ]; If[Length[ps] > 2, t = Join[t, Rest[Most[ps]]]]]; t (* _T. D. Noe_, Apr 30 2012 *)

%Y Cf. A166307, A182365, A166251, A164368, A104272, A080359, A164333, A164288, A164294, A164554, A194598.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Oct 10 2009, Oct 14 2009