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A272143
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For a given n, and any m less than n-1, the total number of primes of the form 2^n-2^m-1.
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2
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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, 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, 2, 3, 0, 9, 1, 5, 2, 5, 8, 3, 0, 10
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OFFSET
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1,4
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COMMENTS
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For the first 12000 terms the average is ~3.8 with a maximum of 25 at a(11520).
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Table[Length[Select[Table[2^n - 2^m - 1, {m, 0, n - 2}], PrimeQ[#] & ]], {n, 1, 100}] (* Robert Price, Apr 21 2016 *)
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PROG
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(Python)
from sympy import isprime
def a(n): return sum(1 for i in range(n-1) if isprime(2**n-1-2**i))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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