A217671 - OEIS

A217671

a(n) is the least prime of the set of the smallest n consecutive primes a(n)=q_1(n), q_2(n),..., such that between (1/2)*q_i and (1/2)q_(i+1), i=1,...,n-1, there exists a prime, or a(n)=0 if no such set of primes exists.

%I #20 Oct 17 2012 13:53:01

%S 3,3,3,73,523,6581,10753,43103,43103,43103,55457,55457,28751773,

%T 278689963,278689963,784284211,4440915607,8340839629,30651695947,

%U 50246427391,50246427391

%N a(n) is the least prime of the set of the smallest n consecutive primes a(n)=q_1(n), q_2(n),..., such that between (1/2)*q_i and (1/2)q_(i+1), i=1,...,n-1, there exists a prime, or a(n)=0 if no such set of primes exists.

%C If a(N) = 0, then a(n) = 0 for n > N. Conjecture 39 in the Shevelev link says that a(n) > 0.

%H V. Shevelev, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL15/Shevelev/shevelev19.html">Ramanujan and Labos primes, their generalizations, and classifications of primes</a>, J. Integer Seq. 15 (2012) Article 12.5.4

%Y Cf. A166251, A182405, A182523, A182426.

%K nonn

%O 2,1

%A _Vladimir Shevelev_, Oct 10 2012

%E a(14) from _John W. Layman_ and _Hans Havermann_

%E a(15)-a(17) from _Carlos Rivera_ and _Hans Havermann_

%E a(18)-a(20) from _Hans Havermann_

%E a(21)-a(22) from _Donovan Johnson_, Oct 17 2012