(Translated by https://www.hiragana.jp/)
A095070 - OEIS
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A095070
One-bit dominant primes, i.e., primes whose binary expansion contains more 1's than 0's.
10
3, 5, 7, 11, 13, 19, 23, 29, 31, 43, 47, 53, 59, 61, 71, 79, 83, 89, 101, 103, 107, 109, 113, 127, 151, 157, 167, 173, 179, 181, 191, 199, 211, 223, 227, 229, 233, 239, 241, 251, 271, 283, 307, 311, 313, 317, 331, 347, 349, 359, 367, 373, 379, 383
OFFSET
1,1
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
Intersection of A000040 and A072600.
Complement of A095075 in A000040.
Subsequence: A095073.
Cf. A095020.
Sequence in context: A138004 A045395 A191377 * A350577 A079733 A179538
KEYWORD
nonn,easy,base
AUTHOR
Antti Karttunen, Jun 01 2004
STATUS
approved