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

1,17

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

Table of n, a(n) for n=1..105.

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: A337086 A113313 A342708 * A182641 A337939 A319020

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