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%I #21 Jun 07 2022 11:12:29
%S 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,
%T 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,
%U 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
%N a(n) is the smallest value of a+b+c for nonnegative integers such that a^b + c = n.
%C An obvious upper bound for this sequence is a(n) <= n-1 because 0^0 + (n-1) = n.
%C 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.
%e a(1) = 0 because 0^0 + 0 = 1 and 0 + 0 + 0 = 0.
%e 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.
%o (Python)
%o def a(n):
%o minSum = n-1
%o for a in range(n-1):
%o for b in range(n-a-1):
%o if a**b>n:
%o break
%o c = n-a**b
%o if a+b+c<minSum:
%o minSum = a+b+c
%o return minSum
%K nonn
%O 1,3
%A _Joshua R. Tint_, May 27 2022
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