cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A192862 #17 May 15 2025 08:18:37
%S A192862 3,5,7,11,13,19,23,29,31,37,41,43,47,59,61,67,73,79,83,101,103,109,
%T A192862 113,127,131,137,139,151,157,163,167,173,181,191,193,211,223,227,229,
%U A192862 239,257,263,271,277,281,283,307,311,313,317,331,347,353,367,373,379
%N A192862 Flat primes: odd primes p such that p+1 is a squarefree number times a power of two.
%C A192862 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.
%H A192862 Charles R Greathouse IV, <a href="/A192862/b192862.txt">Table of n, a(n) for n = 1..10000</a>
%H A192862 Kevin Broughan and Zhou Qizhi, <a href="https://doi.org/10.1017/S0004972710000067">Flat primes and thin primes</a>, Bulletin of the Australian Mathematical Society 82:2 (2010), pp. 282-292.
%H A192862 Qizhi Zhou, <a href="http://researchcommons.waikato.ac.nz/handle/10289/4138">Multiply perfect numbers of low abundancy</a>, PhD thesis (2010)
%F A192862 a(n) ~ k * n * log(n) with k = 1/(2A) = 1.3370563...
%o A192862 (PARI) is(n)=issquarefree((n+1)>>valuation(n+1,2)) && isprime(n) && n>2 \\ _Charles R Greathouse IV_, Mar 26 2014
%Y A192862 Subsequence of A192861.
%Y A192862 Cf. A192863, A192864, A005596.
%K A192862 nonn
%O A192862 1,1
%A A192862 _Charles R Greathouse IV_, Jul 11 2011