A049529 Numbers k such that sum of factorials of digits of k equals pi(k) (A000720).

6500, 6501, 6510, 6511, 6521, 12066, 50372, 175677, 553783, 5224903, 5224923, 5246963, 5302479, 5854093, 5854409, 5854419, 5854429, 5854493, 5855904, 5864049, 5865393, 10990544, 11071599

Offset: 1

Author

G. L. Honaker, Jr., Sep 15 1999

Keywords

• fini
• full
• nonn
• base

Comments

By the time that k = 10^8 the number of primes <= 10^8 (5761455) exceeds 8*9! (2903040). - Robert G. Wilson v, Jan 16 2002

Examples

			a(10)=5224903 because there are exactly 5!+2!+2!+4!+9!+0!+3! (or 363035) prime numbers less than or equal to 5224903.
		

Links

• C. Caldwell and G. L. Honaker, Jr., Is pi(6521)=6!+5!+2!+1! unique?, Math. Spectrum, 22:2 (2000/2001) 34-36.
• Shyam Sunder Gupta, Fascinating Factorials
• Shyam Sunder Gupta, Fascinating Factorials, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 16, 411-442.
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 6521
• Eric Weisstein's World of Mathematics, Factorial

Crossrefs

Cf. A000720, A049530.

Programs

Mathematica

Do[ If[ Apply[ Plus, IntegerDigits[n] ! ] == PrimePi[n], Print[n]], {n, 1, 11100000} ]

PARI

isok(n) = my(d=digits(n)); sum(k=1, #d, d[k]!) == primepi(n); \\ Michel Marcus, Nov 07 2018