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Template:Log^*/doc
From OeisWiki
The {{log^*}} mathematical function template returns the base iterated logarithm of , where is a positive real number and the base is real. (If the number of iterations exceeds 16, an error message is returned!)
Contents
Usage
- {{log^*|a positive real number|base (default e) as a positive real number greater than 1}}
or
- {{log^*|a positive real number|base = base (default e) as a positive real number greater than 1}}
Valid input
- A positive real number as first argument, a positive real number greater than 1 as second argument (base, which defaults to Euler's number e).
Examples
Examples with valid input
Code Result Check Comment {{log^*|1|2}} 0 {{^^|2|0}} = 1 {{log^*|2|2}} 1 {{^^|2|1}} = 2 {{log^*|4|2}} 2 {{^^|2|2}} = 4 {{log^*|16|2}} 3 {{^^|2|3}} = 16 {{log^*|65535|2}} 3 {{log^*|65536|2}} 4 {{^^|2|4}} = 65536 {{log^*|65537|2}} 4 {{log^*|1|3}} 0 {{^^|3|0}} = 1 {{log^*|3|3}} 1 {{^^|3|1}} = 3 {{log^*|26|3}} 1 {{log^*|27|3}} 2 {{^^|3|2}} = 27 {{log^*|28|3}} 2 {{log^*|7625597484986|3}} 2 {{log^*|7625597484987|3}} 3 {{^^|3|3}} = 7625597484987 {{log^*|7625597484988|3}} 3 {{log^*|1}} 0 {{^^|e|0}} = 1 {{log^*|2.718281828459}} 1 {{^^|e|1}} = 2.718281828459 {{log^*|15.154262241479}} 1 {{^^|e|2}} = 15.154262241479 (rounding error issue) {{log^*|15.154262241479*(1+10^(-12))}} 2 {{^^|e|2}} = 15.154262241479 {{log^*|3814279.1047602}} 3 {{^^|e|3}} = 3814279.1047602 {{log^*|INF}} Log^* error: First argument must be a positive real number {{^^|e|4}} = INF (overflow!)
yields
- log ⁎2 65536 = 4
Code Result Check Comment {{log^*|{{^^|e^(1/e)|0}}|e^(1/e)}} 0 {{^^|e^(1/e)|0}} = 1 {{log^*|{{^^|e^(1/e)|1}}|e^(1/e)}} 1 {{^^|e^(1/e)|1}} = 1.4446678610098 {{log^*|{{^^|e^(1/e)|2}}|e^(1/e)}} 2 {{^^|e^(1/e)|2}} = 1.7014206956611 {{log^*|{{^^|e^(1/e)|3}}|e^(1/e)}} 3 {{^^|e^(1/e)|3}} = 1.8699612238031 {{log^*|{{^^|e^(1/e)|4}}|e^(1/e)}} 4 {{^^|e^(1/e)|4}} = 1.9895734917766 {{log^*|{{^^|e^(1/e)|4}}*(1+10^(-12))|e^(1/e)}} 4 {{log^*|{{^^|e^(1/e)|5}}|e^(1/e)}} 4 {{^^|e^(1/e)|5}} = 2.0790752101176 (rounding error issue) {{log^*|{{^^|e^(1/e)|5}}*(1+10^(-12))|e^(1/e)}} 5 {{log^*|{{^^|e^(1/e)|6}}|e^(1/e)}} 6 {{^^|e^(1/e)|6}} = 2.1486699578385 {{log^*|{{^^|e^(1/e)|6}}*(1+10^(-12))|e^(1/e)}} 6 {{log^*|{{^^|e^(1/e)|7}}|e^(1/e)}} 7 {{^^|e^(1/e)|7}} = 2.2043914917479 {{log^*|{{^^|e^(1/e)|7}}*(1+10^(-12))|e^(1/e)}} 7 {{log^*|{{^^|e^(1/e)|8}}|e^(1/e)}} 8 {{^^|e^(1/e)|8}} = 2.2500452117089 {{log^*|{{^^|e^(1/e)|8}}*(1+10^(-12))|e^(1/e)}} 8 {{log^*|{{^^|e^(1/e)|9}}|e^(1/e)}} 9 {{^^|e^(1/e)|9}} = 2.2881539911887 {{log^*|{{^^|e^(1/e)|9}}*(1+10^(-12))|e^(1/e)}} 9 {{log^*|{{^^|e^(1/e)|10}}|e^(1/e)}} 9 {{^^|e^(1/e)|10}} = 2.3204585374295 (rounding error issue) {{log^*|{{^^|e^(1/e)|10}}*(1+10^(-12))|e^(1/e)}} 10 {{log^*|{{^^|e^(1/e)|11}}|e^(1/e)}} 11 {{^^|e^(1/e)|11}} = 2.3481997952302 {{log^*|{{^^|e^(1/e)|11}}*(1+10^(-12))|e^(1/e)}} 11 {{log^*|{{^^|e^(1/e)|12}}|e^(1/e)}} 11 {{^^|e^(1/e)|12}} = 2.372286904328 (rounding error issue) {{log^*|{{^^|e^(1/e)|12}}*(1+10^(-12))|e^(1/e)}} 12 {{log^*|{{^^|e^(1/e)|13}}|e^(1/e)}} 13 {{^^|e^(1/e)|13}} = 2.3934015114452 {{log^*|{{^^|e^(1/e)|13}}*(1+10^(-12))|e^(1/e)}} 13 {{log^*|{{^^|e^(1/e)|14}}|e^(1/e)}} 13 {{^^|e^(1/e)|14}} = 2.4120649600492 (rounding error issue) {{log^*|{{^^|e^(1/e)|14}}*(1+10^(-12))|e^(1/e)}} 14 {{log^*|{{^^|e^(1/e)|15}}|e^(1/e)}} 14 {{^^|e^(1/e)|15}} = 2.4286829379472 (rounding error issue) {{log^*|{{^^|e^(1/e)|15}}*(1+10^(-12))|e^(1/e)}} 15 {{log^*|{{^^|e^(1/e)|16}}|e^(1/e)}} 16 {{^^|e^(1/e)|16}} = 2.4435759555859 {{log^*|{{^^|e^(1/e)|16}}*(1+10^(-12))|e^(1/e)}} 16 {{log^*|{{^^|e^(1/e)|17}}|e^(1/e)}} Expression error: Unrecognized word "excessive". {{^^|e^(1/e)|17}} = 2.4570006473259 (number of iterations exceeds 16) {{log^*|{{^^|e^(1/e)|17}}*(1+10^(-12))|e^(1/e)}} Expression error: Unrecognized word "excessive". (number of iterations exceeds 16)
Examples with invalid input
Code Result {{log^*|9|-3}} Log^* error: Second argument (base) must be a positive real number greater than 1 {{log^*|9|0}} Log^* error: Second argument (base) must be a positive real number greater than 1 {{log^*|9|0.5}} Log^* error: Second argument (base) must be a positive real number greater than 1 {{log^*|9|1}} Log^* error: Second argument (base) must be a positive real number greater than 1 {{log^*|i|3}} Log^* error: First argument must be a positive real number {{log^*|-1|3}} Log^* error: First argument must be a positive real number {{log^*|0|3}} Log^* error: First argument must be a positive real number