A192864 - OEIS

A192864

Lower flat primes: odd primes p such that p-1 is a squarefree number times a power of two.

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. 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