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

1,2

Comments

The sequence is a permutation of the positive integers.

Links

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

Prog

(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

Crossrefs

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

Sequence in context: A085205 A094595 A182830 * A280530 A281280 A281179

Adjacent sequences: A371279 A371280 A371281 * A371283 A371284 A371285

Keyword

nonn

Author

Neal Gersh Tolunsky, Mar 17 2024

Extensions

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

Status

approved