functions.php

/**
 * Force first page of results in archives to an odd number, later pages to an even number
 */
add_action( 'pre_get_posts', 'elodin_change_posts_number_home_page_to_odd' );
function elodin_change_posts_number_home_page_to_odd( $query ) {

    // only modify the query if it's the main query
    if ( !is_admin() && $query->is_main_query() ) {
                        
        $paged = ( get_query_var( 'paged' ) ) ? get_query_var( 'paged' ) : 1;
        
        $postsperpage = get_option( 'posts_per_page' );
                
        // if we're on the first page and the number is even, add one to the number of posts to make it odd
        if ( $paged === 1 && $postsperpage % 2 == 0 ) {
            $postsperpage = $postsperpage + 1;
            $query->set( 'posts_per_page', $postsperpage );
        }
        
        // if the number is even and we're past the first page, then offset by -1
        if (  $paged > 1 && $postsperpage % 2 == 0 ) {
            
            // the offset is the page times the number of pages minus the number on the current page plus one
            $offset = $paged * $postsperpage - $postsperpage + 1;
            $query->set( 'offset', $offset );
        }
        
        if ( $paged == 1 && $postsperpage % 2 != 0 ) {
            // no adjustments needed
        }
        
        // if we're on the first page and the number is even, add one to the number of posts to make it odd
        if ( $paged > 1 && $postsperpage % 2 != 0 ) {
            
            $postsperpage = $postsperpage + 1;
            $query->set( 'posts_per_page', $postsperpage );
            
            // the offset is the page times the number of pages minus the number on the current page minus one
            $offset = $paged * $postsperpage - $postsperpage - 1;
            $query->set( 'offset', $offset );
        }
    }
}