In a specified range, I want to get the number of numbers, in which sum of its digits and sum of squares of its digits are prime number. For an example from 2
to 12
, there are only 2
numbers which has both its sum of digit and sum of square of its digit are prime number. These two numbers are 11
and 12
. In 12
, sum of its digit 1+2=3
and sum of square of its digit 1+4=5
are prime numbers.
Although the question is related to programming but it seems that there must be some number theory trick which can solve it quickly. I am very keen to know that trick if at all exists. Thank you.
Is Sum of digits related with Sum of Squares of its digit
2
$\begingroup$
elementary-number-theory
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2Discussed as a programming problem at http://codereview.stackexchange.com/questions/8319/puzzle-sum-of-the-digits-is-prime-or-not – 2012-04-16
1 Answers
1
Analytic number theory could produce a heuristic for approximately how many numbers up to $x$ satisfy your two conditions (that is, a predicted asymptotic formula), but I doubt it can be proved. Even if it could, it would only give the answer approximately, not exactly as you seem to want. So I don't think there's any trick besides a brute-force calculation.
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0Okay... thanks a ton. – 2012-04-15