A249559 Same definition as A247665, except first term is 3.

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

Offset: 1

Author

N. J. A. Sloane, Nov 02 2014

Keywords

• nonn

Crossrefs

Cf. A247665.

Programs

Python

from itertools import count, islice
from math import gcd
from collections import deque
def A249559_gen(): # generator of terms
    aset, aqueue, c, f = {3}, deque([3]), 2, True
    yield 3
    while True:
        for m in count(c):
            if m not in aset and all(gcd(m,a) == 1 for a in aqueue):
                yield m
                aset.add(m)
                aqueue.append(m)
                if f: aqueue.popleft()
                f = not f
                while c in aset:
                    c += 1
                break
A249559_list = list(islice(A249559_gen(),50)) # Chai Wah Wu, May 19 2022

SageMath

# from Nadia Heninger, Oct 28 2014: s is the starting point (2 in A247665, 3 here).
def gen(s):
    sequence = [s]
    available = range(2, 2*s)
    available.pop(available.index(s))
    yield s
    while True:
        available.extend(range(available[-1]+1, next_prime(available[-1])+1))
        for i, e in enumerate(available):
            if all([gcd(e, sequence[j])==1 for j in range(-len(sequence)/2, 0)]):
                available.pop(i)
                sequence.append(e)
                yield(e)
                break
g = gen(3)
[g.next() for i in range(40)] # gets first 40 terms