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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,17 COMMENTS The first occurrence of k beginning with 0: 1, 2, 17, 59, 337, 779, 16999, 6888888, ..., . - Robert G. Wilson v, Oct 20 2010 LINKS EXAMPLE 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. 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 *) CROSSREFS Cf. A053837, A171765. See A171772 for another version. Sequence in context: A141702 A259896 A113313 * A182641 A319020 A099200 Adjacent sequences:  A074868 A074869 A074870 * A074872 A074873 A074874 KEYWORD easy,nonn,base AUTHOR Felice Russo, Sep 12 2002, Oct 11 2010 EXTENSIONS Edited by N. J. A. Sloane, Oct 12 2010 More terms from Robert G. Wilson v, Oct 20 2010 STATUS approved

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Last modified December 17 00:23 EST 2018. Contains 318191 sequences. (Running on oeis4.)