A095072 Primes in whose binary expansion the number of 0-bits is one more than the number of 1-bits.

17, 67, 73, 97, 263, 269, 277, 281, 293, 337, 353, 389, 401, 449, 1039, 1051, 1063, 1069, 1109, 1123, 1129, 1163, 1171, 1187, 1193, 1201, 1249, 1291, 1301, 1321, 1361, 1543, 1549, 1571, 1609, 1667, 1669, 1697, 1801, 4127, 4157, 4211, 4217

Offset: 1

Author

Antti Karttunen, Jun 01 2004

Keywords

• nonn
• base
• easy

Comments

A010051(a(n)) = 1 and A037861(a(n)) = 1. - Reinhard Zumkeller, Mar 31 2015

Examples

			97 is in the sequence because 97 is a prime and 97_10 = 1100001_2. The number of 0's in 1100001 is 4 and the number of 1's is 3. - _Indranil Ghosh_, Jan 31 2017
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..20000 (terms 1..1000 from Reinhard Zumkeller)
• A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

Crossrefs

Intersection of A000040 and A031444. Subset of A095071.

Cf. A095052.

Cf. A010051, A037861.

Programs

Haskell

a095072 n = a095072_list !! (n-1)
a095072_list = filter ((== 1) . a010051' . fromIntegral) a031444_list
-- Reinhard Zumkeller, Mar 31 2015

Mathematica

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

PARI

isA095072(n)=my(v=binary(n));#v==2*sum(i=1,#v,v[i])+1&&isprime(n)

PARI

forprime(p=2, 4250, v=binary(p); s=0; for(k=1, #v, s+=if(v[k]==0,+1,-1)); if(s==1,print1(p,", ")))

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("0")-bin(i)[2:].count("1")==1:
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Jan 31 2017