Modern solution using java 8 streams:

    Long sum = 0L;        

    for (char digit : n.toCharArray()) {            
        sum += Character.getNumericValue(digit) * k;            
    }

    while(sum.toString().length() > 1) {

        List<String> remainingDigits= String.valueOf(sum)
                                            .chars()
                                            .mapToObj(c -> String.valueOf((char) c))
                                            .collect(Collectors.toList());

        sum = remainingDigits.stream().mapToLong(Long::parseLong).reduce(0L, Long::sum);

    }       

    return sum.intValue();   

}