A095058 - OEIS

%I #26 Dec 23 2023 11:12:20

%S 0,1,2,2,3,0,4,4,3,1,5,1,4,0,3,2,8,1,11,4,5,0,7,1,2,0,1,5,4,0,7,5,1,1,

%T 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,

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

%N Number of primes with a single 0-bit (A095078) in range ]2^n,2^(n+1)].

%C For large n, the average value of a(n) is about 4. See A138290 for the n such that a(n)=0. - _T. D. Noe_, Mar 14 2008

%H T. D. Noe, <a href="/A095058/b095058.txt">Table of n, a(n) for n=1..2048</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 3. - From _N. J. A. Sloane_, Jun 19 2011.

%H Samuel S. Wagstaff, Jr., <a href="http://projecteuclid.org/euclid.em/999188636">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 3.

%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 (PARI) a(n) = sum(k=2^n+1, 2^(n+1), isprime(k) && (#select(x->x==0, binary(k))==1)); \\ _Michel Marcus_, Sep 11 2015

%Y Cf. A095018.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jun 01 2004