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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The Caldwell/Honaker paper does not discuss this, only suggests further areas of investigation.
There are no other members of the sequence up to and including n=1000000. - Harvey P. Dale, Jan 07 2002
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
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!. [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
Sequence in context: A220551 A185073 A185193 * A203515 A166929 A079917
KEYWORD
base,nonn
AUTHOR
Jason Earls, Jan 02 2002
EXTENSIONS
a(7) from Farideh Firoozbakht, Apr 20 2005
a(8)-a(11) from Qu,Shun Liang (medie2006(AT)126.com), Nov 23 2008
a(12) from Chai Wah Wu, May 03 2018
STATUS
approved

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Last modified February 21 03:46 EST 2024. Contains 370219 sequences. (Running on oeis4.)