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.
here, all the elements of this set, except 2 and 5, are SPHN.