A049529 Numbers n such that sum of factorials of digits of n equals pi(n) (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

1,1

Comments

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

Links

Table of n, a(n) for n=1..23.

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

G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 6521

Eric Weisstein's World of Mathematics, Factorial

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000720, A049530.

Sequence in context: A031842 A028544 A237245 * A284102 A338951 A251447

Adjacent sequences: A049526 A049527 A049528 * A049530 A049531 A049532

Keyword

fini,full,nonn,base

Author

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

Status

approved