A390396 - OEIS

%I #17 Nov 15 2025 16:10:38

%S 1,2,4,7,10,13,18,21,24,27,30,33,38,41,44,47,50,53,58,61,64,67,73,78,

%T 81,87,90,93,98,101,104,107,110,113,118,121,124,127,133,138,141,144,

%U 149,155,158,161,172,175,178,181,184,192,195,198,201,204,209,215,218,221,224,229,235

%N Least positive integer not the sum, product or power of any previous pair of distinct terms.

%H Michael S. Branicky, <a href="/A390396/b390396.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n+1) > a(n) for all n > 1 since 1 is a term and hence a(n) is in the set of products and a(n+1) >= a(n) by construction. - _Michael S. Branicky_, Nov 13 2025

%o (Python)

%o from itertools import combinations

%o def generate_sequence(n_terms):

%o     sequence = [1]

%o     while len(sequence) < n_terms:

%o         sums = set()

%o         prods = set()

%o         powers = set()

%o         for a, b in combinations(sequence, 2):

%o             sums.add(a + b)

%o             prods.add(a * b)

%o             try:

%o                 powers.add(a ** b)

%o             except OverflowError:

%o                 pass

%o             try:

%o                 powers.add(b ** a)

%o             except OverflowError:

%o                 pass

%o         forbidden = sums.union(prods).union(powers)

%o         candidate = 1

%o         while candidate in sequence or candidate in forbidden:

%o             candidate += 1

%o         sequence.append(candidate)

%o     return sequence

%o seq = generate_sequence(15)

%o (Python)

%o from math import isqrt

%o from itertools import count

%o def aupto(limit):

%o     alst, an, aset, sums, prds, pows, r = [], 1, {1}, {1}, {1}, set(), isqrt(limit)+1

%o     while an <= limit:

%o         alst.append(an)

%o         aset.add(an)

%o         an = next(k for k in count(an+1) if all(k not in S for S in [sums, prds, pows]))

%o         sums |= {t for s in aset if (t:= an+s) <= limit}

%o         prds |= {t for p in aset if (t:= an*p) <= limit}

%o         for p in aset:

%o             if an > r or (t:=an**p) > limit: break

%o             pows.add(t)

%o         for p in aset:

%o             if p > r or (t:=p**an) > limit: break

%o             pows.add(t)

%o     return alst

%o print(aupto(300)) # _Michael S. Branicky_, Nov 08 2025

%Y Cf. A066512.

%K nonn

%O 1,2

%A _Marc Morgenegg_, Nov 04 2025