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%I #18 Apr 03 2023 10:36:09
%S 6500,6501,6510,6511,6521,12066,50372,175677,553783,5224903,5224923,
%T 5246963,5302479,5854093,5854409,5854419,5854429,5854493,5855904,
%U 5864049,5865393,10990544,11071599
%N Numbers n such that sum of factorials of digits of n equals pi(n) (A000720).
%C By the time that n = 10^8 the number of primes <= 10^8 (5761455) exceeds 8*9! (2903040). - _Robert G. Wilson v_, Jan 16 2002
%H C. Caldwell and G. L. Honaker, Jr., <a href="http://www.utm.edu/staff/caldwell/preprints/6521.pdf">Is pi(6521)=6!+5!+2!+1! unique?</a>, Math. Spectrum, 22:2 (2000/2001) 34-36.
%H Shyam Sunder Gupta, <a href="http://www.shyamsundergupta.com/factorial.htm">Fascinating Factorials</a>
%H G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/992.html">Prime Curios! 6521</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Factorial.html">Factorial</a>
%e a(10)=5224903 because there are exactly 5!+2!+2!+4!+9!+0!+3! (or 363035) prime numbers less than or equal to 5224903.
%t Do[ If[ Apply[ Plus, IntegerDigits[n] ! ] == PrimePi[n], Print[n]], {n, 1, 11100000} ]
%o (PARI) isok(n) = my(d=digits(n)); sum(k=1, #d, d[k]!) == primepi(n); \\ _Michel Marcus_, Nov 07 2018
%Y Cf. A000720, A049530.
%K fini,full,nonn,base
%O 1,1
%A _G. L. Honaker, Jr._, Sep 15 1999
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