

A066457


Numbers n such that product of factorials of digits of n equals pi(n) (A000720).


5



13, 1512, 1520, 1521, 12016, 12035, 226130351, 209210612202, 209210612212, 209210612220, 209210612221, 13030323000581525
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OFFSET

1,1


COMMENTS

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
a(13) > 10^19 if it exists.  Chai Wah Wu, May 03 2018


LINKS

Table of n, a(n) for n=1..12.
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]


EXAMPLE

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]


MATHEMATICA

Select[Range[1000000], Times@@( # !&/@IntegerDigits[ # ])==PrimePi[ # ]&]


PROG

(PARI) isok(n) = my(d = digits(n)); prod(k=1, #d, d[k]!) == primepi(n); \\ Michel Marcus, May 04 2018


CROSSREFS

Cf. A000720, A066459, A049529, A105327.
Sequence in context: A220551 A185073 A185193 * A203515 A166929 A079917
Adjacent sequences: A066454 A066455 A066456 * A066458 A066459 A066460


KEYWORD

base,nonn


AUTHOR

Jason Earls, Jan 02 2002


EXTENSIONS

There are no other members of the sequence up to and including n=1000000.  Harvey P. Dale, Jan 07 2002
226130351 from Farideh Firoozbakht, Apr 20 2005
Four more terms from Qu,Shun Liang (medie2006(AT)126.com), Nov 23 2008
a(12) from Chai Wah Wu, May 03 2018


STATUS

approved



