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Search: id:A066457
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| A066457 |
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Numbers n such that product of factorials of digits of n equals pi(n) (A000720). |
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+0
6
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| 13, 1512, 1520, 1521, 12016, 12035, 226130351, 209210612202, 209210612212, 209210612220, 209210612221
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The Caldwell/Honaker paper does not discuss this, only suggests further areas of investigation.
If 10n is in the sequence and 10n+1 is composite then 10n+1 is also in the sequence (the proof is easy). - Farideh Firoozbakht, Oct 24 2008
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LINKS
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C. Caldwell and G. L. Honaker, Jr., Is pi(6521)=6!+5!+2!+1! unique?
A discussion about this topic: bbs.emath.ac.cn [From Qu,Shun Liang (medie2006(AT)126.com), Nov 23 2008]
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EXAMPLE
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a(5)=12016 because there are exactly 1!*2!*0!*1!*6! (or 1440) prime numbers less than or equal to 12016.
pi(209210612202)=8360755200=2!*0!*9!*2!*1!*0!*6!*1!*2!*2!*0!*2! [From Qu,Shun Liang (medie2006(AT)126.com), Nov 23 2008]
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MATHEMATICA
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Select[Range[1000000], Times@@( # !&/@IntegerDigits[ # ])==PrimePi[ # ]&]
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CROSSREFS
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Cf. A000720, A049529.
Cf. A105327.
Sequence in context: A091781 A156641 A064962 this_sequence A166929 A079917 A028450
Adjacent sequences: A066454 A066455 A066456 this_sequence A066458 A066459 A066460
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KEYWORD
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base,nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Jan 02 2002
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EXTENSIONS
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There are no other members of the sequence up to and including n=1000000. - Harvey P. Dale (hpd1(AT)nyu.edu), Jan 07 2002
226130351 from Farideh Firoozbakht (mymontain(AT)yahoo.com), Apr 20 2005
Four more terms from Qu,Shun Liang (medie2006(AT)126.com), Nov 23 2008
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