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A095018 a(n) is the number of primes p which have exactly n zeros and n ones when written in binary. 10


%S 1,0,2,4,17,28,189,531,1990,5747,23902,76658,291478,982793,3677580,

%T 13214719,49161612

%N a(n) is the number of primes p which have exactly n zeros and n ones when written in binary.

%C a(n) is the number of terms in A066196 which lie between 2^(2n-1) and 2^2n inclusively.

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

%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>

%e a(1) = 1 since only 2_10 = 10_2 satisfies the criterion;

%e a(2) = 0 since there is no prime between 4 and 16 which meets the criterion.

%e The only primes in the range ]2^5,2^6[ with equal numbers of ones and zeros in their binary expansion are 37 (in binary 100101) and 41 (in binary 101011) thus a(3)=2.

%e a(4) = 4 since 139, 149, 163 and 197 meet the criterion; etc.

%t f[n_] := Block[{c = 0, p = NextPrime[2^(2n -1) -1], lmt = 2^(2n)}, While[p < lmt, If[DigitCount[p, 2, 1] == n, c++]; p = NextPrime@ p]; c]; Array[f, 17] (* _K. D. Bajpai_ and _Robert G. Wilson v_, Jan 10 2017 *)

%Y Cf. A066196, A095005, A095006, A095052, A095053, A280872.

%K nonn,base

%O 1,3

%A _Antti Karttunen_, Jun 01 2004

%E Edited by _N. J. A. Sloane_, Jan 16 2017

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Last modified September 26 11:48 EDT 2020. Contains 337371 sequences. (Running on oeis4.)