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A178899 Numbers which are both primes and problimes (third definition).

%I A178899 #20 Nov 20 2020 05:53:12
%S A178899 2,7,11,19,23,43,53,73,79,97,103,109,127,139,151,157,163,181,193,199,
%T A178899 211,1873,1999,2017,2053,2089,2143,2161,2179,2251,2269,2287,2341,2377,
%U A178899 2467,2503,2521,2539,2557,2593,2647,2683,2719,2791,2917,2953,2971,3061,3079
%N A178899 Numbers which are both primes and problimes (third definition).
%H A178899 Alois P. Heinz, <a href="/A178899/b178899.txt">Table of n, a(n) for n = 1..1000</a>
%H A178899 M. D. Hirschhorn, <a href="http://www.jstor.org/stable/2319173">How unexpected is the prime number theorem?</a>, Amer. Math. Monthly, 80 (1973), 675-677.
%H A178899 M. D. Hirschhorn, <a href="/A003066/a003066.pdf">How unexpected is the prime number theorem?</a>, Amer. Math. Monthly, 80 (1973), 675-677. [Annotated scanned copy]
%H A178899 R. C. Vaughan, <a href="http://blms.oxfordjournals.org/content/6/3/337.extract">The problime number theorem</a>, Bull. London Math. Soc., 6 (1974), 337-340.
%F A178899 A000040 INTERSECTION A003068.
%p A178899 b:= proc(n) option remember; local k;
%p A178899       if n=1 then c(2):= 1; 2
%p A178899              else k:= ceil(b(n-1) +1/mul((1-1/b(j)), j=1..n-1));
%p A178899                   c(k):= n; k
%p A178899       fi
%p A178899     end:
%p A178899 a:= proc(n) option remember; local k;
%p A178899       if n=1 then b(1)
%p A178899              else for k from c(a(n-1))+1 while not isprime(b(k))
%p A178899                   do od; b(k)
%p A178899       fi
%p A178899     end:
%p A178899 seq(a(n), n=1..50);  # _Alois P. Heinz_, Dec 29 2010
%t A178899 nmax = 400;
%t A178899 b[n_] := b[n] = If[n==1, 2, Ceiling[b[n-1]+1/Product[1-1/b[j], {j, 1, n-1}]]];
%t A178899 Intersection[Array[b, nmax], Prime[Range[PrimePi[b[nmax]]]]] (* _Jean-François Alcover_, Nov 20 2020 *)
%Y A178899 Cf. A000040, A003068, A178532.
%K A178899 nonn
%O A178899 1,1
%A A178899 _Jonathan Vos Post_, Dec 29 2010
%E A178899 More terms from _Alois P. Heinz_, Dec 29 2010