OFFSET
1,1
COMMENTS
Conjecture: the sequence is infinite.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
EXAMPLE
23 is 10111 in binary, 23 XOR {1,2,4,8,16} = {22,21,19,31,7}, three times a prime was produced, namely 19,31,7, versus two composites, 22 and 21. More primes than composites, therefore 23 is a term.
MAPLE
a:= proc(n) option remember; local k; for k from 1+a(n-1) while add(
`if`(isprime(Bits[Xor](k, 2^i)), 1, -1), i=0..ilog2(k))<1 do od; k
end: a(0):=0:
seq(a(n), n=1..100); # Alois P. Heinz, Dec 07 2017
MATHEMATICA
okQ[n_] := Module[{cnt, f}, cnt = Thread[f[n, 2^Range[0, Log[2, n] // Floor]]] /. f -> BitXor // PrimeQ; Count[cnt, True] > Length[cnt]/2];
Select[Range[1000], okQ] (* Jean-François Alcover, Oct 04 2019 *)
PROG
(Python)
from sympy import isprime
for i in range(1000):
delta = 0 # foundPrime - nonPrime
bit = 1
while bit <= i:
if isprime(i^bit): delta += 1
else: delta -= 1
bit*=2
if delta > 0: print(str(i), end=', ')
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Alex Ratushnyak, Dec 07 2017
STATUS
approved