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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. 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! [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

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Last modified December 19 02:33 EST 2018. Contains 318245 sequences. (Running on oeis4.)