A117135 n-digit primes for which the product of the digits is an n-digit number.

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

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 3-digit prime and (2) the product of its digits 8*7*7=392 is a 3-digit 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