A122863 Smallest integer not the sum of nonzero powers of previous terms.

1, 2, 6, 12, 24, 54, 108, 246, 510, 1218, 2742, 6930, 16242, 47706, 144018, 672732, 2756124, 5656266, 27943404, 75554226, 661653378, 1323306756

Offset

1,2

Comments

At most one power of a previous term is allowed in the sum. Sequence and the first few terms from Andrew Weimholt. Additional terms from Jud McCranie.

It can be shown that a(n) is even for n >= 2 and a(n+1)/a(n) >= 2. Conjecture: lim_{n->infinity} a(n+1)/a(n) = e and lim_{n->infinity} a(n)/e^(n-1) = 1. - Ya-Ping Lu, Feb 18 2022

Links

Table of n, a(n) for n=1..22.

Prog

(Python)
from itertools import product, combinations
def adding(S): T = {n}; {T.add(x + n) for x in S}; W.update(T)
N = []; n_max = 10**9; W = set(); print(1, end = ', ')
for n in range(2, n_max, 2):
    found = False
    for i in range(0, len(N)):
        t = max(N[i])*min(N[i])
        if t == n:
            found = True; M = N[:]; del M[i]; S1 = set()
            {S1.add(sum(c)) for L in product(*M) for j in range(1, len(L)+1) for c in set(combinations(L, j))}
            adding(S1); N[i].add(n)
    if found or n in W: continue
    print(n, end = ', '); adding(W); N.append({n}) # Ya-Ping Lu, Feb 18 2022

Crossrefs

Cf. A034875.

Sequence in context: A197469 A133953 A350293 * A170935 A277173 A163264

Adjacent sequences: A122860 A122861 A122862 * A122864 A122865 A122866

Keyword

nonn

Author

Jud McCranie, Sep 15 2006

Extensions

a(21)-a(22) from Donovan Johnson, Aug 31 2008

Offset corrected by Donovan Johnson, Dec 22 2013

Status

approved