Function Repository Resource:

FindFirstNumberInstance

Source Notebook

Find the first number that matches a certain requirement

Contributed by: Sander Huisman

ResourceFunction["FindFirstNumberInstance"][f]

finds the first integer instance from the range 1 to ∞ for which f returns True

ResourceFunction["FindFirstNumberInstance"][f,max]

finds the first integer instance from the range 1 to max for which f returns True

ResourceFunction["FindFirstNumberInstance"][f,{min, max}]

finds the first integer instance from the range min to max for which f returns True

ResourceFunction["FindFirstNumberInstance"][f,{min,max,step}]

finds the first instance from the range min to max in steps of step for which f returns True

ResourceFunction["FindFirstNumberInstance"][f,spec, n]

finds the first n instances for which f returns True

Details

The third argument n can be set to ∞, and can return all the cases for the case that spec is a finite range.

Unlike in SelectFirst or FirstCase, no upper bound needs to be given.

Examples

Basic Examples (2)

Find the first prime starting from 1:

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Find the first 10 composite numbers:

In[2]:=

$ResourceFunction[ "FindFirstNumberInstance"][CompositeQ, {1, \[Infinity]}, 10]$

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Scope (5)

Find the first 15 square numbers that are a multiple of 7:

In[3]:=

$ResourceFunction["FindFirstNumberInstance"][ IntegerQ@*Sqrt, {0, \[Infinity], 7}, 15]$

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Find the first 15 palindromic primes:

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$ResourceFunction["FindFirstNumberInstance"][ PrimeQ[#] && PalindromeQ[#] &, \[Infinity], 15]$

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Find the first 12 palindromes that are a multiple of 3:

In[5]:=

$ResourceFunction[ "FindFirstNumberInstance"][PalindromeQ, {0, \[Infinity], 3}, 12]$

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Use an iterator with Real step size:

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The iterator can not only be numbers, it can also be a symbolic expression:

In[7]:=

$ResourceFunction["FindFirstNumberInstance"][ Factor[# + x^2 + 4] === # + x^2 + 4 &, {x, 10 x, x}, 5]$

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Possible Issues (2)

FindFirstInstance will return less instances if no more instances exist:

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For the case that there is no third argument and there is no match, FindFirstNumberInstance returns Missing:

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An empty list is returned if there is a third argument:

In[10]:=

$ResourceFunction[ "FindFirstNumberInstance"][# == # + 1 &, {0, 100}, \[Infinity]]$

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Neat Examples (2)

Find the first 12 palindromic composites that are a multiple of 7:

In[11]:=

$ResourceFunction["FindFirstNumberInstance"][ PalindromeQ[#] && CompositeQ[#] &, {0, \[Infinity], 7}, 12]$

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Find the first 20 emirp primes:

In[12]:=

$ResourceFunction["FindFirstNumberInstance"][ PrimeQ[#] && PrimeQ[IntegerReverse[#]] && ! PalindromeQ[#] &, \[Infinity], 20]$

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Publisher

Version History

1.0.1 – 04 October 2022
1.0.0 – 23 September 2022

Related Resources

License Information

This work is licensed under a Creative Commons Attribution 4.0 International License