A192862 Flat primes: odd primes p such that p+1 is a squarefree number times a power of two.

3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 59, 61, 67, 73, 79, 83, 101, 103, 109, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 181, 191, 193, 211, 223, 227, 229, 239, 257, 263, 271, 277, 281, 283, 307, 311, 313, 317, 331, 347, 353, 367, 373, 379

Offset: 1

Author

Charles R Greathouse IV, Jul 11 2011

Keywords

• nonn

Comments

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.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Kevin Broughan and Zhou Qizhi, Flat primes and thin primes, Bulletin of the Australian Mathematical Society 82:2 (2010), pp. 282-292.
• Qizhi Zhou, Multiply perfect numbers of low abundancy, PhD thesis (2010)

Crossrefs

Subsequence of A192861.

Cf. A192863, A192864, A005596.

Programs

PARI

is(n)=issquarefree((n+1)>>valuation(n+1,2)) && isprime(n) && n>2 \\ Charles R Greathouse IV, Mar 26 2014

Formula

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