This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A066457 #35 Mar 19 2025 10:24:47 %S A066457 13,1512,1520,1521,12016,12035,226130351,209210612202,209210612212, %T A066457 209210612220,209210612221,13030323000581525 %N A066457 Numbers k such that product of factorials of digits of k equals pi(k) (A000720). %C A066457 The Caldwell/Honaker paper does not discuss this, only suggests further areas of investigation. %C A066457 There are no other members of the sequence up to and including n=1000000. - _Harvey P. Dale_, Jan 07 2002 %C A066457 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 %C A066457 a(13) > 10^19 if it exists. - _Chai Wah Wu_, May 03 2018 %H A066457 C. Caldwell and G. L. Honaker, Jr., <a href="https://utm.edu/staff/caldwell/preprints/6521.pdf">Is pi(6521)=6!+5!+2!+1! unique?</a> %H A066457 A discussion about this topic: <a href="http://bbs.emath.ac.cn/thread-918-1-1.html">bbs.emath.ac.cn</a> [From Qu,Shun Liang (medie2006(AT)126.com), Nov 23 2008] %H A066457 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_16">Fascinating Factorials</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 16, 411-442. %e A066457 12016 is a term because there are exactly 1!*2!*0!*1!*6! (or 1440) prime numbers less than or equal to 12016. %e A066457 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] %t A066457 Select[Range[1000000], Times@@( # !&/@IntegerDigits[ # ])==PrimePi[ # ]&] %o A066457 (PARI) isok(n) = my(d = digits(n)); prod(k=1, #d, d[k]!) == primepi(n); \\ _Michel Marcus_, May 04 2018 %Y A066457 Cf. A000720, A066459, A049529, A105327. %K A066457 nonn,base,more %O A066457 1,1 %A A066457 _Jason Earls_, Jan 02 2002 %E A066457 a(7) from _Farideh Firoozbakht_, Apr 20 2005 %E A066457 a(8)-a(11) from Qu,Shun Liang (medie2006(AT)126.com), Nov 23 2008 %E A066457 a(12) from _Chai Wah Wu_, May 03 2018