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n-digit primes for which the product of the digits is an n-digit number.
2

%I #8 Jun 24 2019 10:00:48

%S 2,3,5,7,29,37,43,47,53,59,67,73,79,83,89,97,269,349,359,367,379,389,

%T 397,439,449,457,467,479,487,499,547,557,569,577,587,593,599,647,659,

%U 673,677,683,739,757,769,773,787,797,827,829,839,853,857,859,863,877

%N n-digit primes for which the product of the digits is an n-digit number.

%C It is easy to see that the product of the digits of a number does not exceed 9^(log(n)+1) (log is to base 10). On the other hand we can verify that the inequality 9^(log(n)+1) < n/10 holds for all n > 10^43. Hence the sequence is finite. - _Stefan Steinerberger_, Apr 23 2006

%H Giovanni Resta, <a href="/A117135/b117135.txt">Table of n, a(n) for n = 1..10000</a>

%e 877 is in the sequence because (1) it is a 3-digit prime and (2) the product of its digits 8*7*7=392 is a 3-digit number.

%t Select[Prime[Range[1000]], DigitCount[ # ][[10]] == 0 && Length[IntegerDigits[Product[i^DigitCount[ # ][[i]], {i, 1, 9}]]] == Length[IntegerDigits[ # ]] &] (* _Stefan Steinerberger_, Apr 23 2006 *)

%K base,nonn,fini

%O 1,1

%A Luc Stevens (lms022(AT)yahoo.com), Apr 21 2006

%E Corrected by _Stefan Steinerberger_, Apr 23 2006