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

1,1

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A026590 A243413 A222538 * A128349 A255449 A296630

Adjacent sequences: A095070 A095071 A095072 * A095074 A095075 A095076

Keyword

nonn,base,easy

Author

Antti Karttunen, Jun 01 2004

Status

approved