OFFSET
1,1
LINKS
Indranil Ghosh, Table of n, a(n) for n = 1..20000
Antti Karttunen and John Moyer, C-program for computing the initial terms of this sequence.
MathOverflow, Primes with more ones than zeroes in their Binary expansion, 2012.
EXAMPLE
23 is in the sequence because 23 is a prime and 23_10 = 10111_2. '10111' has four 1's and one 0. - Indranil Ghosh, Jan 31 2017
MATHEMATICA
Select[Prime[Range[70]], Plus@@IntegerDigits[#, 2] > Length[IntegerDigits[#, 2]]/2 &] (* Alonso del Arte, Jan 11 2011 *)
Select[Prime[Range[100]], Differences[DigitCount[#, 2]][[1]] < 0 &] (* Amiram Eldar, Jul 25 2023 *)
PROG
(PARI) B(x) = {nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;
for(i = 0, nB, if(bittest(x, i), b1++; , b0++; ); );
if(b1 > b0, return(1); , return(0); ); };
forprime(x = 3, 383, if(B(x), print1(x, ", "); ); ); \\ Washington Bomfim, Jan 11 2011
(PARI) has(n)=hammingweight(n)>#binary(n)/2
select(has, primes(500)) \\ Charles R Greathouse IV, May 02 2013
(Python)
# Program to generate the b-file
from sympy import isprime
i=1
j=1
while j<=200:
if isprime(i) and bin(i)[2:].count("1")>bin(i)[2:].count("0"):
print(str(j)+" "+str(i))
j+=1
i+=1 # Indranil Ghosh, Jan 31 2017
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Antti Karttunen, Jun 01 2004
STATUS
approved