A074871 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.

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, 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, 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

Offset: 1

Author

Felice Russo, Sep 12 2002, Oct 11 2010

Keywords

• easy
• nonn
• base

Comments

The first occurrence of k beginning with 0: 1, 2, 17, 59, 337, 779, 16999, 6888888, ..., . - Robert G. Wilson v, Oct 20 2010

Examples

			T(2)=2. So in one step we reach a prime.
T(3)=3 and then in one step again we reach a prime.
T(4)=4 and we will never reach a prime.
T(11)=1+2=3 and again in one step we reach a prime.
T(17)=7+8=15 --> T(15)=5+6=11 and then in two steps we reach a prime.
T(13)=3+4=7 and then 1 step......
T(14)=4+5=9 --> T(9)=9 --> T(9)=9........ and we will never reach a prime.
		

Crossrefs

Cf. A053837, A171765. See A171772 for another version.

Programs

Mathematica

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 *)

Extensions

Edited by N. J. A. Sloane, Oct 12 2010

More terms from Robert G. Wilson v, Oct 20 2010