A351661 a(n) is the smallest integer m (m > 2n) not the sum of one or more nonzero powers of n, n+1, ..., 2n.

1, 6, 10, 17, 130, 262, 2341, 9576, 144563, 1757032, 9269216, 403525711, 9339823147

Offset

0,2

Comments

a(n) cannot be written as Sum_{i=n..2n} c_i*i^k_i, where c_i = 0 or 1 and k_i is a positive integer.

Links

Table of n, a(n) for n=0..12.

Example

a(2) = 10 because 5 = 2 + 3; 6 = 2 + 4; 7 = 3 + 4; 8 = 2^3; 9 = 3^2 = 2 + 3 + 4; and 10 is the smallest integer > 2*2 not the sum of nonzero powers of 2, 3, and 4.

Prog

(Python)
from itertools import product, combinations
def check(M):
    for L in product(*M):
        for i in range(1, len(L)+1):
            for c in set(combinations(L, i)):
                s = sum(c); W.add(s)
                if s == m: return 1
m_max, R = 10**8, [1]
for n in range(1, 10):
    N, W = [], set()
    for m in range(n, 2*n + 1): N.append({m})
    for m in range(2*n + 1, m_max):
        for i in range(len(N)):
            t = max(N[i])*min(N[i])
            while 1 < t <= m:
                if t == m: W.add(t)
                N[i].add(t); t = max(N[i])*min(N[i])
        if m in W or check(N): continue
        R.append(m); break
print(*R, sep = ', ')

Crossrefs

Cf. A122863, A034875, A351900.

Sequence in context: A049302 A020718 A048587 * A116001 A111617 A315359

Adjacent sequences: A351658 A351659 A351660 * A351662 A351663 A351664

Keyword

nonn,more

Author

Ya-Ping Lu, Feb 19 2022

Extensions

a(10) from Jon E. Schoenfield, Feb 25 2022

a(11)-a(12) from Bert Dobbelaere, Apr 09 2022

Status

approved