%N Flat primes: odd primes p such that p+1 is a squarefree number times a power of two.
%C Broughan & Qizhi show that this sequence has relative density 2A in the primes, where A = A005596 is Artin's constant. Consequently, there exists a flat number between x and (1+e)x for every e > 0 and large enough x.
%H Charles R Greathouse IV, <a href="/A192862/b192862.txt">Table of n, a(n) for n = 1..10000</a>
%H Kevin Broughan and Zhou Qizhi, <a href="http://www.math.waikato.ac.nz/~kab/papers/flatandthin4.pdf">Flat primes and thin primes</a>, Bulletin of the Australian Mathematical Society 82:2 (2010), pp. 282-292.
%H Qizhi Zhou, <a href="http://researchcommons.waikato.ac.nz/handle/10289/4138">Multiply perfect numbers of low abundancy</a>, PhD thesis (2010)
%F a(n) ~ k * n * log(n) with k = 1/(2A) = 1.3370563...
%o (PARI) is(n)=issquarefree((n+1)>>valuation(n+1,2)) && isprime(n) && n>2 \\ _Charles R Greathouse IV_, Mar 26 2014
%Y Subsequence of A192861.
%Y Cf. A192863, A192864, A005596.
%A _Charles R Greathouse IV_, Jul 11 2011