A354153 a(n) is the smallest value of a+b+c for nonnegative integers such that a^b + c = n.

0, 1, 2, 3, 4, 5, 6, 5, 5, 6, 7, 8, 9, 10, 11, 6, 7, 8, 9, 10, 11, 12, 13, 14, 7, 8, 6, 7, 8, 9, 10, 7, 8, 9, 10, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23

Offset

1,3

Comments

An obvious upper bound for this sequence is a(n) <= n-1 because 0^0 + (n-1) = n.

Another upper bound can be defined recursively: a(n) <= a(n-1) + 1 because if n-1 = a^b + c, then n = a^b + c + 1, thus one possible sum is a+b+c+1 or a(n-1) + 1.

Links

Table of n, a(n) for n=1..80.

Example

a(1) = 0 because 0^0 + 0 = 1 and 0 + 0 + 0 = 0.
a(9) = 5 because 3^2 + 0 = 9 and 3 + 2 + 0 = 5 and there is no ordered triple (a,b,c) such that a^b + c = 9 with a+b+c < 5.

Prog

(Python)
def a(n):
    minSum = n-1
    for a in range(n-1):
        for b in range(n-a-1):
            if a**b>n:
                break
            c = n-a**b
            if a+b+c<minSum:
                minSum = a+b+c
    return minSum

Crossrefs

Sequence in context: A017881 A017871 A366259 * A017861 A094700 A073635

Adjacent sequences: A354150 A354151 A354152 * A354154 A354155 A354156

Keyword

nonn

Author

Joshua R. Tint, May 27 2022

Status

approved