A122280 a(1) = 1, a(2) = 2; for n >= 3, a(n) = the smallest positive integer not occurring earlier in the sequence such that gcd(a(n-1), a(n)) is a prime.

1, 2, 4, 6, 3, 9, 12, 10, 5, 15, 18, 8, 14, 7, 21, 24, 22, 11, 33, 27, 30, 16, 26, 13, 39, 36, 34, 17, 51, 42, 20, 25, 35, 28, 38, 19, 57, 45, 40, 46, 23, 69, 48, 50, 32, 54, 44, 55, 60, 58, 29, 87, 63, 49, 56, 62, 31, 93, 66, 52, 65, 70, 64, 74, 37, 111, 72, 75, 78, 68, 82, 41

Offset: 1

Author

Leroy Quet, Aug 29 2006

Keywords

• nonn

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..5002 [Computed using Ray Chandler's Mma program]

Crossrefs

Cf. A122281, A064413.

Programs

Mathematica

f[s_] := Block[{k = 1}, While[MemberQ[s, k] || ! PrimeQ[GCD[Last[s], k]], k++ ]; Append[s, k] ]; Nest[f, {1, 2}, 75] (* Ray Chandler, Aug 30 2006 *)

Python

from math import gcd
from sympy import isprime
from itertools import islice
def agen(): # generator of terms
    aset, an, mink = {1, 2}, 2, 3
    yield from sorted(aset)
    while True:
        k = mink
        while k in aset or not isprime(gcd(an, k)): k += 1
        an = k; aset.add(an); yield an
        while mink in aset: mink += 1
print(list(islice(agen(), 72))) # Michael S. Branicky, Oct 13 2022

Extensions

Extended by Ray Chandler and Klaus Brockhaus, Aug 30 2006