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%I #18 Mar 18 2014 00:01:07
%S 2,3,7,23,31,47,79,127,157,191,223,317,367,379,383,479,727,751,887,
%T 1087,1151,1277,1279,1451,1471,1531,1663,1783,1789,1951,2297,2557,
%U 2927,3067,3259,3319,3581,3583,3967,4253,4349,5119,5231,5503,5807,5821,6079,6143,6271,6653,6871,6911,7039,7103,7151
%N Primes with a binary weight greater than or equal to the binary weight of their squares.
%C Primes p such that A000120(p) = A000120(p^2): 2, 3, 7, 31, 79, 127, 157, 317, 379, 751, 1087, 1151, 1277, 1279,...
%H Charles R Greathouse IV, <a href="/A236514/b236514.txt">Table of n, a(n) for n = 1..10000</a>
%F Primes p such that A000120(p) >= A000120(p^2).
%e 2 is in this sequence because 2 is 10 in binary representation, and it has as many 1s as its square 4, which is 100 in binary.
%t bc[n_] := DigitCount[n, 2][[1]]; Select[Range[7151], PrimeQ[#] && bc[#] >= bc[#^2] &] (* _Giovanni Resta_, Jan 28 2014 *)
%t Select[Prime[Range[1000]], DigitCount[#, 2, 1] >= DigitCount[#^2, 2, 1] &] (* _Alonso del Arte_, Jan 28 2014 *)
%o (PARI) is(n)=hammingweight(n^2)<=hammingweight(n) && isprime(n) \\ _Charles R Greathouse IV_, Mar 18 2014
%Y Cf. A077436, A094694.
%K nonn,base
%O 1,1
%A _Irina Gerasimova_, Jan 27 2014
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