login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A192864 Lower flat primes: odd primes p such that p-1 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 (list; graph; refs; listen; history; text; internal format)
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. 282-292, 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((n-1)>>valuation(n-1, 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 26 15:49 EDT 2021. Contains 346294 sequences. (Running on oeis4.)