

A192862


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


4



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
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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. 282292.
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



