%I #16 Sep 10 2024 18:42:35

%S 3,2,5,7,4,9,11,13,17,19,8,23,15,29,31,37,41,43,47,49,53,59,16,61,67,

%T 71,25,27,73,79,83,89,97,101,103,107,109,113,121,127,91,131,137,139,

%U 149,151,32,157,163,167,173,179,181,191,85,193,57,197,199,211,223,227,229,233,239,241,251,257,263

%N Same definition as A247665, except first term is 3.

%o (SageMath) # from _Nadia Heninger_, Oct 28 2014: s is the starting point (2 in A247665, 3 here).

%o def gen(s):

%o sequence = [s]

%o available = range(2, 2*s)

%o available.pop(available.index(s))

%o yield s

%o while True:

%o available.extend(range(available[-1]+1, next_prime(available[-1])+1))

%o for i, e in enumerate(available):

%o if all([gcd(e, sequence[j])==1 for j in range(-len(sequence)/2, 0)]):

%o available.pop(i)

%o sequence.append(e)

%o yield(e)

%o break

%o g = gen(3)

%o [g.next() for i in range(40)] # gets first 40 terms

%o (Python)

%o from itertools import count, islice

%o from math import gcd

%o from collections import deque

%o def A249559_gen(): # generator of terms

%o aset, aqueue, c, f = {3}, deque([3]), 2, True

%o yield 3

%o while True:

%o for m in count(c):

%o if m not in aset and all(gcd(m,a) == 1 for a in aqueue):

%o yield m

%o aset.add(m)

%o aqueue.append(m)

%o if f: aqueue.popleft()

%o f = not f

%o while c in aset:

%o c += 1

%o break

%o A249559_list = list(islice(A249559_gen(),50)) # _Chai Wah Wu_, May 19 2022

%Y Cf. A247665.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Nov 02 2014