A291777 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,8

LINKS

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

EXAMPLE

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

PROG

(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

CROSSREFS

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