A371282 a(1)=1; for n>1, a(n) = a(n-1) * k or a(n-1) - k to give the smallest, distinct positive integer, where each k can be used only once.

1, 2, 6, 5, 20, 3, 15, 4, 24, 8, 56, 7, 63, 9, 72, 10, 100, 11, 132, 12, 156, 13, 182, 14, 210, 16, 288, 17, 323, 18, 360, 19, 399, 21, 462, 22, 506, 23, 552, 25, 625, 26, 676, 27, 729, 28, 784, 29, 841, 30, 900, 31, 961, 32, 1024, 33, 1089, 34, 1156, 35, 1225

Offset: 1

Author

Neal Gersh Tolunsky, Mar 17 2024

Keywords

• nonn

Comments

The sequence is a permutation of the positive integers.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A371295 (k values), A081145 (add or subtract), A084337 (multiply or divide).

Programs

Python

from itertools import islice
def agen(): # generator of terms
    mina, an, aset, mink, kset = 1, 1, {1}, 1, set()
    while True:
        yield an
        k1, ak1, k2 = 0, mina, mink
        if mina < an:
            for ak1 in range(mina, an-mink+1):
                if ak1 not in aset and an - ak1 not in kset:
                    k1 = an - ak1
                    break
        while k2 in kset or an*k2 in aset:
            k2 += 1
        an, k = (an-k1, k1) if k1 > 0 else (an*k2, k2)
        aset.add(an)
        kset.add(k)
        while mina in aset: mina += 1
        while mink in kset: mink += 1
print(list(islice(agen(), 61))) # Michael S. Branicky, Mar 18 2024

Extensions

a(13) and beyond from Michael S. Branicky, Mar 18 2024