A214617 Primes written in the factorial base.

10, 11, 21, 101, 121, 201, 221, 301, 321, 1021, 1101, 1201, 1221, 1301, 1321, 2021, 2121, 2201, 2301, 2321, 3001, 3101, 3121, 3221, 4001, 4021, 4101, 4121, 4201, 4221, 10101, 10121, 10221, 10301, 11021, 11101, 11201, 11301, 11321, 12021, 12121, 12201, 12321

Offset

1,1

Comments

The factorial base system uses 1!, 2!, 3!, ..., n! instead of powers of b, b^0, b^1, b^2, ... for some base b.

To be consistent with the normal base 10 system, the largest factorial used appears on the left.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

a(n) = A007623(A000040(n)).

Example

prime(6) = 13 = 2*3! + 1! so a(6) = 201.

Maple

b:= proc(n, i) local r; `if`(n<i, n,
      10*b(iquo(n, i, 'r'), i+1)+ r)
    end:
a:= n-> b(ithprime(n), 2):
seq(a(n), n=1..50);  # Alois P. Heinz, Mar 16 2013

Crossrefs

Cf. A000040, A007623.

Sequence in context: A041204 A041202 A324550 * A041200 A041847 A113702

Adjacent sequences: A214614 A214615 A214616 * A214618 A214619 A214620

Keyword

nonn,base

Author

Jon Perry, Mar 06 2013

Status

approved