A166252 Primes which are not the smallest or largest prime in an interval of the form (2*prime(k),2*prime(k+1)).

71, 101, 109, 151, 181, 191, 229, 233, 239, 241, 269, 283, 311, 349, 373, 409, 419, 433, 439, 491, 571, 593, 599, 601, 607, 643, 647, 653, 659, 683, 727, 823, 827, 857, 941, 947, 991, 1021, 1031, 1033, 1051, 1061, 1063, 1091, 1103, 1301, 1373, 1427, 1429

Offset: 1

Author

Vladimir Shevelev, Oct 10 2009, Oct 14 2009

Keywords

• nonn

Comments

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

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

5, k=1

7, k=2

11,13, k=3

17,19, k=4

23, k=5

29,31, k=6

37, k=7

41,43, k=8

47,53, k=9

59,61, k=10

67,71,73, k=11

79, k=12

83, k=13

89, k=14

97,101,103, k=15

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

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

Examples

			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.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Mathematica

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 *)