OFFSET
5,4
COMMENTS
a(4) -> infinity. For any other n >= 2, a(n) is finite, however cases n = 2,3 are trivial, so the offset is 5.
For large n: Sum_{k=5..n} a(k) ~ n*log(n)/2 (conjectured).
LINKS
Yuriy Sibirmovsky, Table of n, a(n) for n = 5..1000
Yuriy Sibirmovsky, Plot of sum_{k=5..n} a(k) for n = 5..20000
EXAMPLE
For n=14: b_0 = 14, not prime. c_0 = 7. b_1 = 7 + 2 = 9. 9 is not prime.
In short: 14 -> {7,2} -> 9 -> {3,3} -> 6 -> {3,2} -> 5. Number of runs a(14) = 3.
MATHEMATICA
Nm=100;
a=Table[0, {n, 1, Nm}];
Do[b0=n;
j=0;
While[PrimeQ[b0]==False, c=Reverse[Divisors[b0]];
b1=c[[2]]+b0/c[[2]];
b0=b1; j++];
a[[n]]=j, {n, 5, Nm}];
Table[a[[k]], {k, 5, Nm}]
PROG
(PARI) stop(n) = (n<=1) || isprime(n);
a(n) = {b = n; nb = 0; while (! stop(b), d = divisors(b); c = d[#d-1]; b = c + b/c; nb++; ); nb; } \\ Michel Marcus, Sep 19 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Yuriy Sibirmovsky, Sep 17 2016
STATUS
approved