A374527 Odd numbers whose Collatz trajectory is a Sidon sequence.

1, 21, 85, 151, 227, 341, 1365, 5461, 14563, 21845, 87381, 349525, 932067, 1398101, 5592405, 22369621, 26512143, 39768215, 59652323, 89478485, 357913941, 1431655765, 3817748707, 5726623061

Offset: 1

Author

Markus Sigg and Hugo Pfoertner, Jul 27 2024

Keywords

• nonn
• hard
• more

Comments

For more information see A375006.

Crossrefs

Odd terms of A375006.

Programs

Python

from itertools import count, islice
def A374527_gen(startvalue=1): # generator of terms >= startvalue
    s = max(startvalue,1)
    for n in count(s+(s&1^1),2):
        t, a, c = [n], n, set()
        while a > 1:
            a = 3*a+1 if a&1 else a>>1
            for p in t:
                if (b:=p+a) in c:
                    break
                c.add(b)
            else:
                t.append(a)
                continue
            break
        else:
            yield n
A374527_list = list(islice(A374527_gen(),10)) # Chai Wah Wu, Jul 27 2024

Extensions

a(23)-a(24) from Chai Wah Wu, Jul 29 2024