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%I #10 Jul 19 2015 01:17:07
%S 0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,2,1,0,1,1,0,1,0,1,2,1,2,1,1,1,1,2,1,
%T 1,2,2,2,1,0,0,0,1,0,1,0,1,2,2,1,1,1,1,1,2,1,1,1,3,0,1,2,2,0,1,3,2,2,
%U 1,1,2,1,2,1,1,2,1,1,2,0,1,2,2,2,1,2,1,2,1,0,0,1,1,2,3,1,2,1,1,0,1,1,0,1,0
%N Start with n and repeatedly apply the map k -> T(k) = A053837(k) + A171765(k); a(n) is the number of steps (at least one) until a prime is reached, or 0 if no prime is ever reached.
%C The first occurrence of k beginning with 0: 1, 2, 17, 59, 337, 779, 16999, 6888888, ..., . - _Robert G. Wilson v_, Oct 20 2010
%e T(2)=2. So in one step we reach a prime.
%e T(3)=3 and then in one step again we reach a prime.
%e T(4)=4 and we will never reach a prime.
%e T(11)=1+2=3 and again in one step we reach a prime.
%e T(17)=7+8=15 --> T(15)=5+6=11 and then in two steps we reach a prime.
%e T(13)=3+4=7 and then 1 step......
%e T(14)=4+5=9 --> T(9)=9 --> T(9)=9........ and we will never reach a prime.
%t g[n_] := Block[{id = IntegerDigits@ n}, Mod[ Plus @@ id, 10] + If[n < 10, 0, Times @@ id]]; f[n_] := Block[{lst = Rest@ NestWhileList[g, n, UnsameQ, All]}, lsp = PrimeQ@ lst; If[ Last@ Union@ lsp == False, 0, Position[lsp, True, 1, 1][[1, 1]]]]; Array[f, 105] (* _Robert G. Wilson v_, Oct 20 2010 *)
%Y Cf. A053837, A171765. See A171772 for another version.
%K easy,nonn,base
%O 1,17
%A _Felice Russo_, Sep 12 2002, Oct 11 2010
%E Edited by _N. J. A. Sloane_, Oct 12 2010
%E More terms from _Robert G. Wilson v_, Oct 20 2010
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