A291777 a(n) = number of steps to reach a prime when x -> sigma(x)-1 is repeatedly applied to 2^n-1, or -1 if no prime is ever reached.

0, 0, 1, 0, 1, 0, 1, 3, 2, 9, 2, 0, 7, 3, 4, 0, 2, 0, 1, 4, 1, 4, 2, 3, 4, 2, 12, 22, 8, 0, 3, 3, 4, 3, 1, 2, 2, 3, 3, 4, 3, 13, 2, 16, 3, 8, 3, 14, 17, 9, 37, 4, 7, 4, 7, 11, 4, 3, 14, 0, 14, 8, 1, 6, 8, 73, 26, 10, 1, 32, 6, 10, 2, 6, 2, 33, 2, 4, 52, 12, 16

Offset: 2

Author

N. J. A. Sloane, Aug 31 2017

Keywords

• nonn

Examples

			For n=9, 2^n-1 = 511 with iterates 511->591->791->911, and 911 is the first prime, so a(7)=3.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 2..270

Crossrefs

Cf. A039654, A039655, A291301, A291302, A291776.

Programs

PARI

C(x) = {for(c=0,10^5,if(isprime(x),return(c),x=sigma(x)-1));-1}
vector(200,n,C(2^(n+1)-1)) \\ Lars Blomberg, Sep 01 2017

Extensions

a(13)-a(82) from Lars Blomberg, Sep 01 2017