A164767 Primes obtained from other primes by taking the factorial of each digit and adding them up.

2, 7, 7, 3, 727, 13, 13, 31, 127, 727, 727, 5, 5, 11, 37, 362911, 151, 40351, 362911, 151, 5881, 5881, 1447, 6481, 364321, 5167, 15121, 408241, 408241, 408241, 1088641, 5, 5, 11, 11, 7, 362911, 733, 11, 19, 19, 733, 37, 751, 362911, 5167, 151, 5167, 733, 733

Offset

1,1

Comments

The primes are considered in increasing order.

For the first 100 million primes, the first 50 primes are formed. Do all primes eventually appear? - Robert G. Wilson v, Aug 31 2009

Links

Table of n, a(n) for n=1..50.

Example

The prime 11 gives, 1! + 1! = 2 (prime). The prime 163 gives, 1! + 6! + 3! = 727 (prime). The prime 613 gives, 6! + 1! + 3! = 727 (prime).

Mathematica

f[n_] := Plus @@ (IntegerDigits@n!); lst = {}; Do[p = Prime@n; a = f@p; If[ PrimeQ@a && a != p, AppendTo[lst, a]], {n, 10^3}]; lst (* Robert G. Wilson v, Aug 31 2009 *)
Select[Total[IntegerDigits[#]!]&/@Prime[Range[1000]], PrimeQ] (* Harvey P. Dale, Jan 03 2016 *)

Crossrefs

Cf. A000040, A164676.

Sequence in context: A153649 A020770 A177003 * A244645 A277527 A188636

Adjacent sequences: A164764 A164765 A164766 * A164768 A164769 A164770

Keyword

base,nonn

Author

Parthasarathy Nambi, Aug 25 2009

Extensions

More terms from Robert G. Wilson v, Aug 31 2009

Status

approved