Hence if the number is reversed, the sum of digits remains same , and then, the new number is also SPHN.
Now, it is sufficient to find the square of the sum of digits of any number to test its SPHN status.
For example, 13200432175211431501 is a SPHN, because sum of digits of this 20--digit number is 46; and [46'.
All the SPHN are concatenated one after another and the new number is tested.
k] [member of] , if k is odd, and hence it a SPHN [member of] , if k is even.
i+k] [member of] , if k is even, and it is a SPHN , if k is odd.
Therefore the product of numbers in each twin pair is SPHN.
Then we note that the status of SPHN changes with the base.
6] [member of] ; Hence 35 is SPHN at the base 6 also.
9] [member of] ; Hence 89 is SPHN at the base 9.
However, some numbers, which are not SPHN with base 10, become SPHN with change of base, as: 49 = [(100).
Lemma Square of any natural number n is SPHN with ref.