A095283 Primes whose binary-expansion ends with an odd number of 1's.

5, 7, 13, 17, 23, 29, 31, 37, 41, 53, 61, 71, 73, 89, 97, 101, 103, 109, 113, 127, 137, 149, 151, 157, 167, 173, 181, 193, 197, 199, 223, 229, 233, 241, 257, 263, 269, 277, 281, 293, 311, 313, 317, 337, 349, 353, 359, 373, 383, 389, 397, 401, 409

Offset: 1

Author

Antti Karttunen, Jun 04 2004

Keywords

• nonn
• base
• easy

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

Crossrefs

Intersection of A000040 & A079523. Complement of A095282 in A000040. Cf. A027697, A095293.

Programs

Maple

q:= proc(n) local i, l, r; l, r:= convert(n, base, 2), 0;
      for i to nops(l) while l[i]=1 do r:=r+1 od; is(r, odd)
    end:
select(q, [ithprime(i)$i=1..150])[];  # Alois P. Heinz, Dec 15 2019

Mathematica

Select[Prime[Range[100]], MatchQ[IntegerDigits[#, 2], {b:(1)..}|{_, 0, b:(1)..} /; OddQ[Length[{b}]]]&] (* Jean-François Alcover, Jan 03 2022 *)

PARI

is(n)=valuation(n+1,2)%2 && isprime(n) \\ Charles R Greathouse IV, Oct 09 2013

Python

from sympy import isprime
def ok(n): b = bin(n); return (len(b)-len(b.rstrip("1")))%2 and isprime(n)
print([k for k in range(1, 401) if ok(k)]) # Michael S. Branicky, Jan 03 2022