OFFSET
1,1
COMMENTS
Comment from Vladimir Shevelev, Jun 01 2007: Conjecture: If pi_1(m) is the number of a(n) not exceeding m and pi_2(m) is the number of A027697(n) not exceeding m then pi_1(m) <= smaller than pi_2(m) for all natural m except m=5 and m=6. I verified this conjecture up to 10^9. Moreover I conjecture that pi_2(m)-pi_1(m) tends to infinity with records at the primes m=2, 13, 41, 61, 67, 79, 109, 131, 137, ...
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
E. Fouvry, C. Mauduit, Sommes des chiffres et nombres presque premiers, (French) [Sums of digits and almost primes] Math. Ann. 305 (1996), no. 3, 571--599. MR1397437 (97k:11029).
V. Shevelev, A conjecture on primes and a step towards justification, arXiv:0706.0786 [math.NT], 2007.
MATHEMATICA
Select[Prime[Range[200]], EvenQ[Count[IntegerDigits[ #, 2], 1]]&] (* T. D. Noe, Jun 12 2007 *)
PROG
(PARI) forprime(p=1, 999, norml2(binary(p))%2 || print1(p", "))
(PARI) isA027699(p)=isprime(p) && !bittest(norml2(binary(p)), 0) \\ M. F. Hasler, Dec 12 2010
(Python)
from sympy import isprime
def ok(n): return bin(n).count("1")%2 == 0 and isprime(n)
print([k for k in range(812) if ok(k)]) # Michael S. Branicky, Jun 27 2022
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
EXTENSIONS
More terms from Erich Friedman
STATUS
approved