A276771 a(n) is the number of runs of an algorithm. Set b_0 = n, if prime or 1 or 0, stop; else, set c_0 = largest divisor of n (!=n); set b_1 = c_0 - b_0/c_0. Run with b_1.
0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 2, 0, 1, 0, 2, 2, 2, 0, 2, 1, 1, 2, 3, 0, 1, 0, 2, 2, 2, 1, 3, 0, 1, 2, 2, 0, 1, 0, 3, 3, 3, 0, 3, 1, 1, 2, 3, 0, 2, 2, 2, 3, 3, 0, 4, 0, 1, 2, 2, 2, 1, 0, 3, 3, 3, 0, 3, 0, 2, 3, 4, 2, 1, 0, 2, 3, 3, 0, 3, 3, 1, 2, 2, 0, 1, 2, 4, 4, 4, 2, 4, 0, 1, 2, 4
Offset: 1
Keywords
Examples
For n=14: b_0 = 14, not prime or 1 or 0. c_0 = 7. b_1 = 7 - 2 = 5. 5 is prime.
In short: 14 -> {7,2} -> 5. Number of runs a(14) = 1.
Links
- Yuriy Sibirmovsky, Table of n, a(n) for n = 1..1000
- Yuriy Sibirmovsky, Plot of sum_{k=1..n} a(k) for n = 1..20000
Programs
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Mathematica
Nm=100; a=Table[0,{n,1,Nm}]; Do[b0=n; j=0; While[PrimeQ[b0]==False&&b0!=1&&b0!=0,c=Reverse[Divisors[b0]]; b1=c[[2]]-b0/c[[2]]; b0=b1;j++]; a[[n]]=j,{n,1,Nm}]; a -
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
Comments