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

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, 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, 2, 3, 0, 9, 1, 5, 2, 5, 8, 3, 0, 10, 3, 0, 2, 4, 4, 6

Offset: 1

Author

Reinhard Zumkeller, Feb 23 2012

Keywords

• nonn

Comments

Number of primes in (n-1)-st row of the triangle in A081118;

a(A138290(n)+1) = 0;

for n >= 0: a(A208091(n)) = n and a(m) <> n for m < A208091(n).

Examples

			n _ A208083(n) ________________ (n-1)-st row of A081118 _________
5   #{23,29} = 2                [15,23,27,29]
6   #{31,47,59,61} = 4          [31,47,55,59,61]
7   #{} = 0                     [63,95,111,119,123,125]
8   #{127,191,223,239,251} = 5  [127,191,223,239,247,251,253]
9   #{383,479,503,509} = 4      [255,383,447,479,495,503,507,509]
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1500

Crossrefs

Cf. A010051, A081118, A138290, A181741, A208091.

Programs

Haskell

a208083 = sum . map a010051 . a081118_row

Maple

f:= n -> nops(select(k -> isprime(2^n-2^k-1),[$1..n-1])):
map(f, [$1..100]); # Robert Israel, Jun 12 2018

Mathematica

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 *)

PARI

a(n)=sum(k=1,n-1,ispseudoprime(2^n-2^k-1)) \\ Charles R Greathouse IV, Sep 12 2013

Formula

a(n) = Sum_{k=1..n-1} A010051(A081118(n-1,k)).