add_action( 'genesis_after_entry', 'sk_insert_post' );
function sk_insert_post() {

	global $wp_query;

	if ( is_main_query() && is_home() && 0 == get_query_var( 'paged' ) && 0 == $wp_query->current_post ) {
		echo "string";
	}

}

add_action( 'pre_get_posts', 'myprefix_query_offset', 1 );
function myprefix_query_offset( &$query ) {

	// Before anything else, make sure this is the right query...
	if ( ! $query->is_home() ) {
		return;
	}

	// First, define your desired offset...
	$offset = -1;

	// Next, determine how many posts per page you want (we'll use WordPress's settings)
	$ppp = get_option( 'posts_per_page' );

	// Next, detect and handle pagination...
	if ( $query->is_paged ) {

		// Manually determine page query offset (offset + current page (minus one) x posts per page)
		$page_offset = $offset + ( ($query->query_vars['paged']-1) * $ppp );

		// Apply adjust page offset
		$query->set( 'offset', $page_offset );

	}
	else {

		// This is the first page. Set a different number for posts per page
		$query->set( 'posts_per_page', $offset + $ppp );

	}
}

add_filter( 'found_posts', 'myprefix_adjust_offset_pagination', 1, 2 );
function myprefix_adjust_offset_pagination( $found_posts, $query ) {

	// Define our offset again...
	$offset = -1;

	// Ensure we're modifying the right query object...
	if ( $query->is_home() ) {
		// Reduce WordPress's found_posts count by the offset...
		return $found_posts - $offset;
	}
	return $found_posts;
}