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

1,1

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A091930 A124526 A124418 * A303951 A326776 A249746

Adjacent sequences: A175174 A175175 A175176 * A175178 A175179 A175180

Keyword

nonn

Author

Artur Jasinski, Mar 01 2010

Extensions

Name clarified by Hugo Pfoertner, Sep 23 2017

Status

approved