|
%I #19 Aug 03 2014 14:01:31
%S 3,5,7,11,13,19,23,31,37,43,47,61,67,73,79,103,127,151,157,163,191,
%T 193,211,223,271,277,283,313,331,367,383,397,421,457,463,487,523,541,
%U 547,607,613,631,661,673,691,733,751,757,787,823,877,907,991,997,1051
%N Thin primes: odd primes p such that p+1 is a prime (or 1) times a power of two.
%C Broughan & Qizhi conjecture that a(n) << n (log n)^2, matching the lower bound they proved.
%C Sequence A206581 excludes the Mersenne primes (A000043), which are included here under the "or 1" case. - T. D. Noe, Mar 07 2012
%D D. R. Heath-Brown, "Artin's conjecture for primitive roots", Quarterly Journal of Mathematics 37:1 (1986) pp. 27-38.
%D N. M. Timofeev, "The Hardy-Ramanujan and Halasz inequalities for shifted primes", Mathematical Notes 57:5 (1995), pp. 522-535.
%H T. D. Noe, <a href="/A192869/b192869.txt">Table of n, a(n) for n = 1..1000</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) >> n (log n)^2.
%t onePrimeQ[n_] := n == 1 || PrimeQ[n]; Select[Prime[Range[2, 1000]], onePrimeQ[(# + 1)/2^IntegerExponent[# + 1, 2]] &] (* _T. D. Noe_, Mar 06 2012 *)
%o (PARI) is(n)=n%2&&isprime(n)&&(isprime((n+1)>>valuation(n+1,2)) || n+1==1<<valuation(n+1,2))
%Y Subsequence of A192868.
%K nonn
%O 1,1
%A _Charles R Greathouse IV_, Jul 11 2011
|
