A165198 Primes from integers by taking the factorial of each digit and adding them up.

2, 2, 2, 3, 7, 3, 3, 7, 7, 3, 3, 3, 3, 5, 13, 31, 127, 727, 31, 127, 241, 727, 45361, 45361, 5, 5, 5, 5, 13, 31, 127, 727, 13, 31, 127, 727, 13, 13, 31, 31, 127, 127, 727, 727, 31, 31, 31, 31, 127, 241, 127, 241, 127, 127, 241, 241, 727, 727, 727, 727, 45361, 45361, 45361

Offset

1,1

Comments

The integers are considered in increasing order.

All primes eventually appear. Least integer k which produces the n-th prime: 2, 12, 122, 13, 1223, 133, 12233, 1333, 122333, 1224, 134, 1334, 122334, 13334, 1223334, ..., . - Robert G. Wilson v, Sep 30 2009

Links

Table of n, a(n) for n=1..63.

Dario Alpern, Factorization using the Elliptic Curve Method

Example

2 from 11 by 1! + 1!.
3 from 100 by 1! + 0! + 0!
13 from 133 by 1! + 3! + 3!
727 from 136 by 1! + 3! + 6!
45361 from 178 by 1! + 7! + 8!
155->241. 178->45361. 1223->11. 1224->29. 1333->19. 1334->37. 1336->733. 1345->151. - R. J. Mathar, Sep 17 2009

Mathematica

f[n_] := Plus @@ (IntegerDigits@ n!); k = 0; lst = {}; While[k < 783, a = f@k; If[ PrimeQ@a, AppendTo[lst, a]]; k++ ]; lst (* Robert G. Wilson v, Sep 30 2009 *)

Crossrefs

Cf. A061602. - R. J. Mathar, Sep 17 2009

Sequence in context: A091712 A125721 A049798 * A245526 A024682 A091228

Adjacent sequences: A165195 A165196 A165197 * A165199 A165200 A165201

Keyword

base,nonn

Author

Parthasarathy Nambi, Sep 07 2009

Extensions

2! = 2 and 10 -> 1! + 0! = 2 prepended by R. J. Mathar, Sep 17 2009

Status

approved