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%I #10 Aug 28 2020 07:05:48
%S 1,1,2,3,3,5,5,4,6,5,8,5,7,6,7,7,10,8,9,8,11,12,10,12,14,10,15,13,13,
%T 17,16,16,17,14,18,18,17,22,18,22,16,21,23,20,20,24,22,24,26,23,23,26,
%U 25,26,25,28,25,31,29,26,31,27,28,31,32,31,37,32,29,32,34,31,35,34,32
%N Number of primes of the form floor( (1+1/k)^n ), 1<=k<=n.
%H Amiram Eldar, <a href="/A072923/b072923.txt">Table of n, a(n) for n = 1..10000</a>
%F Conjecture: a(n) is asymptotic to C*n with C = 0.47......
%e floor((1+1/k)^15 is prime for k = 7,8,11,12,13,14,15 (giving the successive prime values 7,5,3,3,3,2,2) hence a(15) = 7.
%t a[n_] := Count[Floor[(1 + 1/Range[n])^n], _?PrimeQ]; Array[a, 100] (* _Amiram Eldar_, Aug 28 2020 *)
%o (PARI) a(n)=if(n<0,0,sum(k=1,n,if(isprime(floor((1+1/k)^n)),1,0)))
%K easy,nonn
%O 1,3
%A _Benoit Cloitre_, Aug 11 2002
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