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Number of 1's required to build n using + and ^
2

%I #14 Oct 09 2021 15:55:24

%S 1,2,3,4,5,6,7,5,5,6,7,8,9,10,11,6,7,8,9,10,11,12,13,11,7,8,6,7,8,9,

%T 10,7,8,9,10,8,9,10,11,12,12,13,12,13,13,14,15,13,9,10,11,12,13,12,13,

%U 14,14,14,13,14,15,16,14,7,8,9,10,11,12,13,14,12,12,13,14,15,16,17

%N Number of 1's required to build n using + and ^

%H Glen Whitney, <a href="/A348262/b348262.txt">Table of n, a(n) for n = 1..10000</a>

%H Edinah K. Ghang and Doron Zeilberger, <a href="https://arxiv.org/abs/1303.0885">Zeroless Arithmetic: Representing Integers ONLY using ONE</a>, arXiv:1303.0885 [math.CO], 2013.

%H Glen Whitney, <a href="/A348262/a348262.py.txt">Python3.8 program to compute a(n)</a>

%H <a href="/index/Com#complexity">Index to sequences related to the complexity of n</a>

%F a(n) = (A213924(n) + 1)/2.

%e 11+111++^ is a minimal-length RPN formula with value 8, using just these operators. It contains five occurrences of the symbol "1". Hence, a(8) = 5.

%Y Cf. A213924 (expression-length complexity with the same set {1,+,^}).

%Y Cf. A025280 (operand complexity (minimum number of ones) for {1,+,*,^}).

%K nonn

%O 1,2

%A _Glen Whitney_, Oct 09 2021