

A192864


Lower flat primes: odd primes p such that p1 is a squarefree number times a power of two.


3



3, 5, 7, 11, 13, 17, 23, 29, 31, 41, 43, 47, 53, 59, 61, 67, 71, 79, 83, 89, 97, 103, 107, 113, 131, 137, 139, 149, 157, 167, 173, 179, 191, 193, 211, 223, 227, 229, 233, 239, 241, 257, 263, 269, 277, 281, 283, 293, 311, 313, 317, 331, 337, 347, 349, 353, 359
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OFFSET

1,1


COMMENTS

Broughan & Qizhi show that this sequence has relative density 2*A 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.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000
Kevin A. Broughan and Zhou Qizhi, Flat primes and thin primes, Bulletin of the Australian Mathematical Society, Vol. 82, No. 2 (2010), pp. 282292, alternative link.


FORMULA

a(n) ~ k * n * log(n) with k = 1/(2*A) = 1.3370563...


MATHEMATICA

Select[Range[3, 360, 2], PrimeQ[#] && SquareFreeQ[(#  1)/2^IntegerExponent[#  1, 2]] &] (* Amiram Eldar, Aug 30 2020 *)


PROG

(PARI) is(n)=n%2&&isprime(n)&&issquarefree((n1)>>valuation(n1, 2)) \\ corrected by Amiram Eldar, Aug 30 2020


CROSSREFS

Subsequence of A192863.
Cf. A192861, A192862, A005596.
Sequence in context: A090670 A074832 A075794 * A135832 A074781 A147545
Adjacent sequences: A192861 A192862 A192863 * A192865 A192866 A192867


KEYWORD

nonn


AUTHOR

Charles R Greathouse IV, Jul 11 2011


EXTENSIONS

Data corrected by Amiram Eldar, Aug 30 2020


STATUS

approved



