A095287 Primes in whose binary expansion the number of 1-bits is <= 1 + number of 0-bits.

2, 5, 17, 19, 37, 41, 67, 71, 73, 83, 89, 97, 101, 113, 131, 137, 139, 149, 163, 193, 197, 257, 263, 269, 271, 277, 281, 283, 293, 307, 313, 331, 337, 353, 389, 397, 401, 409, 419, 421, 433, 449, 457, 521, 523, 541, 547, 557, 563, 569, 577, 587, 593, 601, 613

Offset: 1

Author

Antti Karttunen, Jun 04 2004

Keywords

• nonn
• base
• easy

Examples

			From _Indranil Ghosh_, Feb 03 2017: (Start)
5 is in the sequence because 5_10 = 101_2. '101' has two 1's and one 0.
17 is in the sequence because 17_10 = 10001_2. '10001' has two 1's and three 0's. (End)
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..25000
• A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

Crossrefs

Complement of A095286 in A000040. Subset: A095075. Subset of A095315. Cf. also A095297.

Programs

Mathematica

Select[Prime[Range[200]],DigitCount[#,2,1]<=1+DigitCount[#,2,0]&] (* Harvey P. Dale, Apr 18 2023 *)

PARI

forprime(p=2,613,v=binary(p);s=0;for(k=1,#v,s+=if(v[k]==1,+1,-1));if(s<=1,print1(p,", "))) \\ Washington Bomfim, Jan 13 2011

Python

from sympy import isprime
i=1
j=1
while j<=250:
    if isprime(i) and bin(i)[2:].count("1")<=1+bin(i)[2:].count("0"):
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Feb 03 2017