login
A095283
Primes whose binary-expansion ends with an odd number of 1's.
4
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
1,1
LINKS
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 *)
PROG
(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
CROSSREFS
Intersection of A000040 & A079523. Complement of A095282 in A000040. Cf. A027697, A095293.
Sequence in context: A216735 A216771 A216690 * A317543 A253297 A163385
KEYWORD
nonn,base,easy
AUTHOR
Antti Karttunen, Jun 04 2004
STATUS
approved