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

Offset

1,1

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

Example

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. (Stop)

Mathematica

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

Prog

(PARI)forprime(p=2, 587, 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

Crossrefs

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

Sequence in context: A215425 A205511 A215276 * A020608 A075612 A156010

Adjacent sequences: A095284 A095285 A095286 * A095288 A095289 A095290

Keyword

nonn,base,easy

Author

Antti Karttunen, Jun 04 2004

Status

approved