# [seqfan] Verifying A074871, iteration of sum-of-digits(n)+product-of-digits(n)

Richard Mathar mathar at strw.leidenuniv.nl
Sun Oct 10 14:05:23 CEST 2010

```Which definition can explain the numbers in A074871?
http://oeis.org/classic/A074871
Using n -> and counting steps a(n) to reach a prime, the definition
of setting a(n)=0 if primes are never reached is strange, because
if n itself is prime, that number of steps is 0.
Also, there are currently primes p for which a(p)=1 and others for which a(p)=2.
So setting

a(n) is the number of steps of reaching a prime under the map
n -> A061762(n), -1 if no prime is reached, I get with offset 1:
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
Example: a(4)=3 because 4->8->16->13 is prime.
Example: a(39)=-1 because 39 -> 39 ->39 .. never reaches a prime.
Example: a(49)=-1 because 49 -> 49 ->49 .. never reaches a prime.
Example: a(69)=-1 because 69 -> 69 ->69 .. never reaches a prime.
Example: a(74)=-1 because 74 -> 39 ->39 .. never reaches a prime.
Funny that this seems to coincide with the example in the sequence at a(28).

The author of the sequence is not on a carbon copy list because
katamail.com responds with an error message addressing that account.

RJM

```