editing

approved

The first occurrence of k beginning with 0: 1, 2, 17, 59, 337, 779, 16999, 6888888, ..., . [From _- _Robert G. Wilson v_, Oct 20 2010]

T(14)=4+5=9 --> T(9)=9 --> T(9)=9........ and we will never reach a prime.

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] [From _(* _Robert G. Wilson v_, Oct 20 2010] *)

approved

editing

proposed

approved

editing

proposed

_Felice Russo (felice.russo(AT)katamail.com), _, Sep 12 2002, Oct 11 2010

approved

editing

Edited by _N. J. A. Sloane, _, Oct 12 2010

The first occurrence of k beginning with 0: 1, 2, 17, 59, 337, 779, 16999, 6888888, ..., . [From _Robert G. Wilson v (rgwv(AT)rgwv.com), _, Oct 20 2010]

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] [From _Robert G. Wilson v (rgwv(AT)rgwv.com), _, Oct 20 2010]

More terms from _Robert G. Wilson v (rgwv(AT)rgwv.com), _, Oct 20 2010

0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 0, 1, 0, 1, 2, 1, 3, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 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

The first occurrence of k beginning with 0: 1, 2, 17, 59, 337, 779, 16999, 6888888, ..., . [From Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 20 2010]

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] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 20 2010]

easy,nonn,base,more,new

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 20 2010

Number Start with n and repeatedly apply the map k -> T(k) = A053837(k) + A171765(k); a(n) is the number of steps needed to reach (at least one) until a prime when the map S(n)+M(n) is applied to n; reached, or 0 if a no prime is never ever reached. Here S(n) and M(N) mean the sum and the product of the digits of n in base 10.

a(28)=3 because 28 ->26 ->20 ->2

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

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

easy,nonn,base,more,new

Felice Russo (felice.russo(AT)katamail.com), Sep 12 2002, Oct 11 2010

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

Number of steps needed to reach a prime when the map S(n)+M(n) is applied to n; 0 if a prime is never reached. Here S(n) and M(N) mean the sum and the product of the digits of n in base 10.

0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 0, 1, 2, 1, 3, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 0, 1

1,17

a(28)=3 because 28 ->26 ->20 ->2

easy,nonn,base

Felice Russo (felice.russo(AT)katamail.com), Sep 12 2002

approved