A095073 Primes in whose binary expansion the number of 1-bits is one more than the number of 0-bits.

5, 19, 71, 83, 89, 101, 113, 271, 283, 307, 313, 331, 397, 409, 419, 421, 433, 457, 1103, 1117, 1181, 1223, 1229, 1237, 1303, 1307, 1319, 1381, 1427, 1429, 1433, 1481, 1489, 1559, 1579, 1607, 1613, 1619, 1621, 1637, 1699, 1733, 1811, 1861

Offset: 1

Author

Antti Karttunen, Jun 01 2004

Keywords

• nonn
• base
• easy

Examples

			71 is in the sequence because 71_10 = 1000111_2. '1000111' has four 1's and three 0's. - _Indranil Ghosh_, Feb 03 2017
		

Links

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

Crossrefs

Intersection of A000040 and A031448. Subset of A095070. Cf. A095053.

Programs

Mathematica

Select[Prime[Range[500]], Differences[DigitCount[#, 2]] == {-1} &]

PARI

{ forprime(p=2, 2000,
  v=binary(p); s=0;
  for(k=1,#v, s+=if(v[k]==1,+1,-1));
  if(s==1,print1(p,", "))
) }

Python

from sympy import isprime
i=1
j=1
while j<=25000:
    if isprime(i) and bin(i)[2:].count("1")-bin(i)[2:].count("0")==1:
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Feb 03 2017