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

1,4

Comments

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

Links

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

Example

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.

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

Crossrefs

A variant of A074871.

Cf. A007954, A053837, A061762.

Sequence in context: A260737 A059339 A241181 * A092735 A035464 A194669

Adjacent sequences: A171769 A171770 A171771 * A171773 A171774 A171775

Keyword

base,easy,sign

Author

R. J. Mathar, Oct 12 2010

Status

approved