A171772 Number of steps needed to reach a prime when the map S(n)+M(n) is applied to n, or -1 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.

1, 0, 0, 3, 0, 2, 0, 2, 2, 2, 0, 1, 0, 3, 1, 1, 0, 1, 0, 1, 1, 3, 0, 4, 1, 2, 1, 3, 0, 1, 0, 1, 2, 1, 1, 2, 0, 2, -1, 4, 0, 4, 0, 5, 1, 2, 0, 6, -1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 3, 0, 2, 2, 2, 1, 7, 0, 3, -1, 1, 0, 1, 0, -1, 1, 3, 3, 1, 0, 3

Offset: 1

Author

R. J. Mathar, Oct 12 2010

Keywords

• base
• easy
• sign

Comments

a(n)=0 if n is a prime.

Examples

			a(4)=3 because 4->8->16->13 is prime.
a(39)=-1 because 39 -> 39 ->39 ... never reaches a prime.
a(49)=-1 because 49 -> 49 ->49 ... never reaches a prime.
a(69)=-1 because 69 -> 69 ->69 ... never reaches a prime.
a(74)=-1 because 74 -> 39 ->39 ... never reaches a prime.
a(28)=3 because 28 ->26 ->20 ->2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

A variant of A074871.

Cf. A007954, A053837, A061762.

Programs

Maple

f:= proc(n) local L;
  L:= convert(n,base,10);
  convert(L,`+`)+convert(L,`*`);
end proc:
g:= proc(n) option remember; local v,w;
     if n::prime then return 0 fi;
     v:= f(n);
     if v = n then return -1 fi;
     w:= procname(v);
     if w = -1 then -1 else w+1 fi
end proc:
map(g, [$1..100]); # Robert Israel, Nov 03 2019