

A117135


ndigit primes for which the product of the digits is an ndigit number.


2



2, 3, 5, 7, 29, 37, 43, 47, 53, 59, 67, 73, 79, 83, 89, 97, 269, 349, 359, 367, 379, 389, 397, 439, 449, 457, 467, 479, 487, 499, 547, 557, 569, 577, 587, 593, 599, 647, 659, 673, 677, 683, 739, 757, 769, 773, 787, 797, 827, 829, 839, 853, 857, 859, 863, 877
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000


EXAMPLE

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


MATHEMATICA

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


CROSSREFS

Sequence in context: A211660 A215155 A228486 * A332582 A019372 A117299
Adjacent sequences: A117132 A117133 A117134 * A117136 A117137 A117138


KEYWORD

base,nonn,fini


AUTHOR

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


EXTENSIONS

Corrected by Stefan Steinerberger, Apr 23 2006


STATUS

approved



