A349491 a(1)=1, a(2)=4; for n > 2, a(n) is the smallest unused positive number such that gcd(a(n-1)*n,a(n)) > 1, where a(n) != a(n-1) and a(n) != n.

1, 4, 2, 6, 3, 8, 10, 5, 12, 9, 15, 14, 7, 16, 18, 20, 22, 11, 33, 21, 24, 26, 13, 27, 30, 25, 35, 32, 28, 34, 17, 36, 38, 19, 40, 39, 42, 44, 45, 46, 23, 48, 50, 52, 51, 54, 56, 49, 63, 55, 57, 58, 29, 60, 62, 31, 66, 64, 68, 65, 70, 72, 69, 74, 37, 75, 78, 76, 80, 77, 84, 81, 87

Offset: 1

Author

Scott R. Shannon, Nov 19 2021

Keywords

• nonn

Comments

This sequence shows similar behavior to the EKG sequence A064413. See the linked image.

Examples

			a(3) = 2 as a(2)*3 = 6, 2!=4, 2!=3, 2 is unused and gcd(6,2) > 1.
a(4) = 6 as a(3)*4 = 8, 6!=2, 6!=4, 6 is unused and gcd(8,6) > 1.
		

Links

• Scott R. Shannon, Image of the first 10000 terms. The green line is y = n.

Crossrefs

Cf. A064413, A349493, A349472, A098550, A336957.

Programs

Python

from math import gcd
terms, appears = [1], {}
for n in range(2, 100):
    t = 2
    while not(appears.get(t) is None and gcd(terms[-1]*n, t)>1 and t!=terms[-1] and t!=n):
        t += 1
    appears[t] = True; terms.append(t);
print(terms) # Gleb Ivanov, Nov 20 2021