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A214617 Primes written in the factorial base.

%I A214617 #28 Mar 18 2013 18:28:25
%S A214617 10,11,21,101,121,201,221,301,321,1021,1101,1201,1221,1301,1321,2021,
%T A214617 2121,2201,2301,2321,3001,3101,3121,3221,4001,4021,4101,4121,4201,
%U A214617 4221,10101,10121,10221,10301,11021,11101,11201,11301,11321,12021,12121,12201,12321
%N A214617 Primes written in the factorial base.
%C A214617 The factorial base system uses 1!, 2!, 3!, ..., n! instead of powers of b, b^0, b^1, b^2, ... for some base b.
%C A214617 To be consistent with the normal base 10 system, the largest factorial used appears on the left.
%H A214617 Alois P. Heinz, <a href="/A214617/b214617.txt">Table of n, a(n) for n = 1..1000</a>
%F A214617 a(n) = A007623(A000040(n)).
%e A214617 prime(6) = 13 = 2*3! + 1! so a(6) = 201.
%p A214617 b:= proc(n, i) local r; `if`(n<i, n,
%p A214617       10*b(iquo(n, i, 'r'), i+1)+ r)
%p A214617     end:
%p A214617 a:= n-> b(ithprime(n), 2):
%p A214617 seq(a(n), n=1..50);  # _Alois P. Heinz_, Mar 16 2013
%Y A214617 Cf. A000040, A007623.
%K A214617 nonn,base
%O A214617 1,1
%A A214617 _Jon Perry_, Mar 06 2013