A175177 Conjectured number of numbers for which the iteration x -> phi(x) + 1 terminates at prime(n). Cardinality of rooted tree T_p (where p is n-th prime) in Karpenko's book.

2, 3, 4, 9, 2, 31, 6, 4, 2, 2, 2, 11, 24, 41, 2, 2, 2, 57, 2, 2, 58, 2, 2, 6, 17, 4, 2, 2, 39, 67, 2, 2, 2, 2, 2, 2, 25, 4, 2, 2, 2, 158, 2, 61, 2, 2, 2, 2, 2, 2, 54, 2, 186, 2, 10, 2, 2, 2, 18, 8, 2, 2, 2, 2, 96, 2, 2, 18, 2, 6, 15, 2, 2, 2, 2, 2, 2, 44, 34, 6, 2, 16, 2, 105, 2, 2, 60, 5, 4, 2, 2, 2, 4

Offset: 1

Author

Artur Jasinski, Mar 01 2010

Keywords

• nonn

Examples

			a(3) = 4 because x = { 5, 8, 10, 12 } are the 4 numbers from which the iteration x -> phi(x) + 1 terminates at prime(3) = 5.
a(4) = 8 because x = { 7, 9, 14, 15, 16, 18, 20, 24, 30 } are the 9 numbers from which the iteration x -> phi(x) + 1 terminates at prime(4) = 7.
		

References

• Richard K. Guy, Unsolved Problems in Number Theory, Third Edition, Springer, New York 2004. Chapter B41, Iterations of phi and sigma, page 148.
• A. S. Karpenko, Lukasiewicz's Logics and Prime Numbers, (English translation), 2006. See Table 2 on p.125 ff.
• A. S. Karpenko, Lukasiewicz's Logics and Prime Numbers, (Russian), 2000.

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A039649, A039650, A039651, A039652, A096827, A175178.

Programs

PARI

iterat(x) = {my(k,s); if ( isprime(x),return(x)); s=x;
for (k=1,1000000000,s=eulerphi(s)+1;if(isprime(s),return(s)));
return(s); }
check(y,endrange) = {my(count,start); count=0;
for(start=1,endrange,if(iterat(start)==y,count++;));
return(count); }
for (n=1,93,x=prime(n);print1(check(x,1000000),", "))
\\ Hugo Pfoertner, Sep 23 2017

Extensions

Name clarified by Hugo Pfoertner, Sep 23 2017