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A208083 Number of primes of the form 2^n - 2^k - 1, 1 <= k < n.

%I A208083 #23 Dec 21 2022 20:21:11
%S A208083 0,0,2,3,2,4,0,5,4,3,1,5,1,5,0,3,2,9,1,12,4,5,0,7,1,2,0,1,5,4,0,8,5,1,
%T A208083 1,9,0,6,0,7,1,6,0,4,7,2,1,10,3,3,1,2,1,6,0,4,3,0,1,8,3,4,0,3,1,8,1,2,
%U A208083 2,3,0,9,1,5,2,5,8,3,0,10,3,0,2,4,4,6
%N A208083 Number of primes of the form 2^n - 2^k - 1, 1 <= k < n.
%C A208083 Number of primes in (n-1)-st row of the triangle in A081118;
%C A208083 a(A138290(n)+1) = 0;
%C A208083 for n >= 0: a(A208091(n)) = n and a(m) <> n for m < A208091(n).
%H A208083 Robert Israel, <a href="/A208083/b208083.txt">Table of n, a(n) for n = 1..1500</a>
%F A208083 a(n) = Sum_{k=1..n-1} A010051(A081118(n-1,k)).
%e A208083 n _ A208083(n) ________________ (n-1)-st row of A081118 _________
%e A208083 5   #{23,29} = 2                [15,23,27,29]
%e A208083 6   #{31,47,59,61} = 4          [31,47,55,59,61]
%e A208083 7   #{} = 0                     [63,95,111,119,123,125]
%e A208083 8   #{127,191,223,239,251} = 5  [127,191,223,239,247,251,253]
%e A208083 9   #{383,479,503,509} = 4      [255,383,447,479,495,503,507,509]
%p A208083 f:= n -> nops(select(k -> isprime(2^n-2^k-1),[$1..n-1])):
%p A208083 map(f, [$1..100]); # _Robert Israel_, Jun 12 2018
%t A208083 a[n_] := Module[{m = 2^n - 1, cnt = 0}, For[ k = 1, k < n, k++, If[PrimeQ[m - 2^k], cnt++]]; cnt]; Table[a[n], {n, 2, 86}] (* _Jean-François Alcover_, Sep 12 2013 *)
%o A208083 (Haskell)
%o A208083 a208083 = sum . map a010051 . a081118_row
%o A208083 (PARI) a(n)=sum(k=1,n-1,ispseudoprime(2^n-2^k-1)) \\ _Charles R Greathouse IV_, Sep 12 2013
%Y A208083 Cf. A010051, A081118, A138290, A181741, A208091.
%K A208083 nonn
%O A208083 1,3
%A A208083 _Reinhard Zumkeller_, Feb 23 2012