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%I #13 Feb 21 2024 01:21:23
%S 11,101,211,311,1021,1201,1301,1321,2011,2111,2221,2311,3001,3011,
%T 3121,3221,3301,4001,4021,4111,4201,4211,10111,10211,10301,10321,
%U 11311,11321,12011,12101,12211,12301,13001,13121,14011,14221,14321,20011,20021,20101,20201,21001
%N Prime values of integers written in factorial base, interpreted as in base 10.
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%e a(1) = 11 = 1*(2!) + 1*(1!) = A007623(3)_10.
%e a(2) = 101 = 1*(3!) + 0*(2!) + 1*(1!) = A007623(7)_10.
%e a(3) = 211 = 2*(3!) + 1*(2!) + 1*(1!) = A007623(15)_10.
%e a(4) = 311 = 3*(3!) + 1*(2!) + 1*(1!) = A007623(21)_10.
%e a(5) = 1021 = 1*(4!) + 0*(3!) + 2*(2!) + 1*(1!) = A007623(29)_10.
%e a(6) = 1201 = 1*(4!) + 2*(3!) + 0*(2!) + 1*(1!) = A007623(37)_10.
%e a(7) = 1301 = 1*(4!) + 3*(3!) + 0*(2!) + 1*(1!) = A007623(43)_10.
%e a(8) = 1321 = 1*(4!) + 3*(3!) + 2*(2!) + 1*(1!) = A007623(47)_10.
%t f[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; FromDigits[Reverse @ s]]; Select[Array[f, 300], PrimeQ] (* _Amiram Eldar_, Feb 21 2024 *)
%Y Cf. A007623 (Integers written in factorial base).
%K base,easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Sep 06 2006
%E More terms from _Amiram Eldar_, Feb 21 2024
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