cp's OEIS Frontend

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.

%I A171772 #11 Nov 03 2019 19:48:36
%S A171772 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,
%T A171772 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,
%U A171772 3,-1,1,0,1,0,-1,1,3,3,1,0,3
%N 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.
%C A171772 a(n)=0 if n is a prime.
%H A171772 Robert Israel, <a href="/A171772/b171772.txt">Table of n, a(n) for n = 1..10000</a>
%e A171772 a(4)=3 because 4->8->16->13 is prime.
%e A171772 a(39)=-1 because 39 -> 39 ->39 ... never reaches a prime.
%e A171772 a(49)=-1 because 49 -> 49 ->49 ... never reaches a prime.
%e A171772 a(69)=-1 because 69 -> 69 ->69 ... never reaches a prime.
%e A171772 a(74)=-1 because 74 -> 39 ->39 ... never reaches a prime.
%e A171772 a(28)=3 because 28 ->26 ->20 ->2.
%p A171772 f:= proc(n) local L;
%p A171772   L:= convert(n,base,10);
%p A171772   convert(L,`+`)+convert(L,`*`);
%p A171772 end proc:
%p A171772 g:= proc(n) option remember; local v,w;
%p A171772      if n::prime then return 0 fi;
%p A171772      v:= f(n);
%p A171772      if v = n then return -1 fi;
%p A171772      w:= procname(v);
%p A171772      if w = -1 then -1 else w+1 fi
%p A171772 end proc:
%p A171772 map(g, [$1..100]); # _Robert Israel_, Nov 03 2019
%Y A171772 A variant of A074871.
%Y A171772 Cf. A007954, A053837, A061762.
%K A171772 base,easy,sign
%O A171772 1,4
%A A171772 _R. J. Mathar_, Oct 12 2010