Customized title tag for each page in pagination?

Do you use a query to display results on each page?

If you know the query arguments then you can do stuff based on the output. Let’s say 'posts_per_page' is set to 20. You can use found_posts to count how many posts there are, and show a title tag based on that info:

$num_posts = $my_query->found_posts;

// For index pages
if(is_page('page_title_here') && $num_posts / 20 == 4){
     // Now you're on page 4
}

// For category pages
if(is_category('category_title_here') && $num_posts / 20 == 3){
     // Now you're on page 3
}

If you have 'paged' set to $paged and you’ve defined $paged = (get_query_var('paged')) ? get_query_var('paged') : 1; then you can make if statements based on the page number (nicer than the above code IMO):

// For index pages
if(is_page('page_title_here') && $paged == 4){
     // Now you're on page 4
}

// For category pages
if(is_category('category_title_here') && $paged == 3){
     // Now you're on page 3
}

I’m actually not sure what you mean by title tags, but you can do anything you like in within the if statements.

UPDATE

If you want the code to put the title in the <title> tag in the <head> section, wrap the code in a function:

function title_function(){
    // For index pages
    if(is_page('page_title_here') && $paged == 4){
         return 'Title for page 4 on page_title_here';
    }

    // For category pages
    if(is_category('category_title_here') && $paged == 3){
         return 'Title for page 3 on category_title_here';
    }
}

And put

<title><?php echo title_function(); ?></title>

UPDATE 2

I misread the question, instead of is_page in the code above, use is_home() if your page shows recent posts, or is_front_page() if your homepage is a static page:

function title_function(){
    // For homepage
    if(is_home() && $paged == 4){
         return 'Title for page 4 on page_title_here';
    }

    // For category pages
    if(is_category('category_title_here') && $paged == 3){
         return 'Title for page 3 on category_title_here';
    }
}

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