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 A099053 a(n) is the smallest number of 1s and 2s that are needed to construct n using any number of +, -, *, ^ signs but not allowing concatenation of digits. 2
 1, 1, 2, 2, 3, 3, 4, 3, 3, 4, 4, 4, 5, 4, 4, 3, 4, 4, 5, 5, 6, 5, 5, 5, 4, 5, 4, 5, 5, 5, 5, 4, 5, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Subexpressions can be grouped as needed; equivalently, any number of parentheses can be used in the expression. Yet another definition of the complexity of a number. It can be assumed that no subexpression can be <= 0. The only way to generate a negative value is to take a-b with a < b; taking b-a instead gives the absolute value of this expression. For any further number generated using the negative value, the absolute value of that number is obtainable using the absolute value of the subexpression(s). Generating an intermediate zero is useless. - Franklin T. Adams-Watters, Jul 29 2011 LINKS EXAMPLE 1 = 1, so has complexity 1. 2 = 2, so has complexity 1. 3 = 1+2, so has complexity 2. 4 = 2+2 = 2*2 = 2^2, so has complexity 2. 5 = 2+1+2, so has complexity 3. ... 16 = 2^2^2, so has complexity 3. CROSSREFS Positions of records are given in A060274. Sequence in context: A067693 A322006 A173419 * A230697 A322163 A075167 Adjacent sequences:  A099050 A099051 A099052 * A099054 A099055 A099056 KEYWORD nonn,more AUTHOR Tim Peters (tim.one(AT)comcast.net), Nov 14 2004 STATUS approved

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)