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%I #16 Sep 02 2023 04:15:44
%S 0,1,1,5,6,11,24,37,67,124,223,382
%N Number of primitive weird numbers (A002975) between 10^n and 10^(n+1).
%C It is not known unconditionally whether there are infinitely many primitive weird numbers (PWN, A002975), although numerical data provides strong evidence: even the number of weird numbers of the form 2^k*p*q (A258882, A258333) seems to increase rapidly as k increases. Melfi has shown that Cramer's conjecture implies the infiniteness of PWN.
%H Giuseppe Melfi, <a href="http://dx.doi.org/10.1016/j.jnt.2014.07.024">On the conditional infiniteness of primitive weird numbers</a>, Journal of Number Theory, Volume 147, February 2015, Pages 508-514.
%o (PARI) a(n)=sum(n=10^n\2+1,5*10^n,is_A002975(n*2))
%Y Cf. A002975, A006037, A258333, A258882, A275491, A275493, A275494.
%K nonn,more
%O 0,4
%A _M. F. Hasler_, Jul 30 2016
%E Wrong initial term removed and a(11) added by _Amiram Eldar_, Sep 02 2023
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