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A272143 For a given n, and any m less than n-1, the total number of primes of the form 2^n-2^m-1.

%I A272143 #16 Nov 09 2023 08:55:00
%S A272143 0,1,1,2,2,3,0,4,4,3,1,5,1,4,0,3,2,8,1,11,4,5,0,7,1,2,0,1,5,4,0,7,5,1,
%T A272143 1,9,0,6,0,7,1,6,0,4,7,2,1,10,3,3,1,2,1,6,0,4,3,0,1,8,3,3,0,3,1,8,1,2,
%U A272143 2,3,0,9,1,5,2,5,8,3,0,10
%N A272143 For a given n, and any m less than n-1, the total number of primes of the form 2^n-2^m-1.
%C A272143 For the first 12000 terms the average is ~3.8 with a maximum of 25 at a(11520).
%C A272143 Essentially the same as A095058. - _R. J. Mathar_, Apr 24 2016
%H A272143 Hans Havermann, <a href="/A272143/b272143.txt">Table of n, a(n) for n = 1..12000</a>
%H A272143 Hans Havermann, <a href="http://chesswanks.com/num/a095078.txt">Table of n, {m1, m2, ...} for primes of the form 2^n-2^m-1, m<n-1.</a>
%e A272143 For n=1, m<0, so there are no solutions. For n=2 there is one solution: m=0, yielding prime 2. For n=3, one solution: m=1, yielding prime 5. For n=4 there are two solutions: m=2 and m=1, yielding primes 11 and 13 respectively. The primes so formed are terms of A095078.
%t A272143 Table[Length[Select[Table[2^n - 2^m - 1, {m, 0, n - 2}], PrimeQ[#] & ]], {n, 1, 100}] (* _Robert Price_, Apr 21 2016 *)
%o A272143 (Python)
%o A272143 from sympy import isprime
%o A272143 def a(n): return sum(1 for i in range(n-1) if isprime(2**n-1-2**i))
%o A272143 print([a(n) for n in range(1, 81)]) # _Michael S. Branicky_, Nov 09 2023
%Y A272143 Cf. A095078.
%K A272143 nonn
%O A272143 1,4
%A A272143 _Hans Havermann_, Apr 21 2016