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

1,1

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)

Formula

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

Prog

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

Crossrefs

Subsequence of A192861.

Cf. A192863, A192864, A005596.

Sequence in context: A071329 A109358 A216285 * A110589 A138004 A045395

Adjacent sequences: A192859 A192860 A192861 * A192863 A192864 A192865

Keyword

nonn

Author

Charles R Greathouse IV, Jul 11 2011

Status

approved