A095059 - OEIS

%I #22 Dec 27 2023 14:34:15

%S 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 37,45,47,0,69,31,36,34,55,34,71,10,60,50,69,22,81,52,59,5,97,71,79,

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

%H Michael S. Branicky, <a href="/A095059/b095059.txt">Table of n, a(n) for n = 1..1000</a>

%H A. Karttunen and J. Moyer, <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>

%H 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 <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 (Python)

%o from sympy import isprime

%o from itertools import combinations, count, islice

%o def a(n): # generator of terms

%o     if n < 2: return 0

%o     b, d = (1<<n+1)-1, n-1

%o     return sum(1 for i, j in combinations(range(d), 2) if isprime(b-(1<<(d-i))-(1<<(d-j))))

%o print([a(n) for n in range(1, 100)]) # _Michael S. Branicky_, Dec 27 2023

%Y Cf. A095018, A095056, A095057, A095058.

%K base,nonn

%O 1,5

%A _Antti Karttunen_, Jun 01 2004

%E Added terms a(34)-a(99) from the Wagstaff paper. - _N. J. A. Sloane_, Jun 19 2011