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A095059 Number of primes with two 0-bits (A095079) in range ]2^n,2^(n+1)].

%I A095059 #22 Dec 27 2023 14:34:15
%S A095059 0,0,0,1,2,4,0,9,5,14,4,16,9,18,0,21,21,21,7,41,22,31,5,37,20,33,14,
%T A095059 37,45,47,0,69,31,36,34,55,34,71,10,60,50,69,22,81,52,59,5,97,71,79,
%U A095059 42,67,86,95,13,103,61,81,47,98,50,110,0,108,87,116,36,125,98,98,29,126,90,125,46,107,100,125,8,158,81,109,65,156,94,131,27,127,144,146,38,167,129,137,6,127,112,178,76
%N A095059 Number of primes with two 0-bits (A095079) in range ]2^n,2^(n+1)].
%H A095059 Michael S. Branicky, <a href="/A095059/b095059.txt">Table of n, a(n) for n = 1..1000</a>
%H A095059 A. Karttunen and J. Moyer, <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095059 Samuel S. Wagstaff, Jr., <a href="http://www.emis.de/journals/EM/expmath/volumes/10/10.html">Prime Numbers with a fixed number of one bits or zero bits in their binary representation</a>, Exp. Math. vol. 10, issue 2 (2001) 267, Table 4. - From _N. J. A. Sloane_, Jun 19 2011.
%H A095059 <a href="/index/Pri#primesubsetpop2">Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]</a>
%o A095059 (Python)
%o A095059 from sympy import isprime
%o A095059 from itertools import combinations, count, islice
%o A095059 def a(n): # generator of terms
%o A095059     if n < 2: return 0
%o A095059     b, d = (1<<n+1)-1, n-1
%o A095059     return sum(1 for i, j in combinations(range(d), 2) if isprime(b-(1<<(d-i))-(1<<(d-j))))
%o A095059 print([a(n) for n in range(1, 100)]) # _Michael S. Branicky_, Dec 27 2023
%Y A095059 Cf. A095018, A095056, A095057, A095058.
%K A095059 base,nonn
%O A095059 1,5
%A A095059 _Antti Karttunen_, Jun 01 2004
%E A095059 Added terms a(34)-a(99) from the Wagstaff paper. - _N. J. A. Sloane_, Jun 19 2011