

A165198


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


0



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
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OFFSET

1,1


COMMENTS

The integers are considered in increasing order.
All primes eventually appear. Least integer k which produces the nth 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



