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Search: id:A117135
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| A117135 |
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n-digit primes for which the product of the digits is an n-digit number. |
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+0
1
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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 (stefan.steinerberger(AT)gmail.com), Apr 23 2006
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EXAMPLE
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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.
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MATHEMATICA
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Select[Prime[Range[1000]], DigitCount[ # ][[10]] == 0 && Length[IntegerDigits[Product[i^DigitCount[ # ][[i]], {i, 1, 9}]]] == Length[IntegerDigits[ # ]] &] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 23 2006
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CROSSREFS
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Sequence in context: A085907 A024777 A002957 this_sequence A019372 A117299 A091924
Adjacent sequences: A117132 A117133 A117134 this_sequence A117136 A117137 A117138
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KEYWORD
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base,nonn,fini
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AUTHOR
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Luc Stevens (lms022(AT)yahoo.com), Apr 21 2006
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EXTENSIONS
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Corrected by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 23 2006
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