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A175177
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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.
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5
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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
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OFFSET
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1,1
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REFERENCES
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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.
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LINKS
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Hugo Pfoertner, Table of n, a(n) for n = 1..1000
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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Cf. A039649, A039650, A039651, A039652, A096827, A175178.
Sequence in context: A091930 A124526 A124418 * A303951 A326776 A249746
Adjacent sequences: A175174 A175175 A175176 * A175178 A175179 A175180
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski, Mar 01 2010
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EXTENSIONS
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Name clarified by Hugo Pfoertner, Sep 23 2017
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STATUS
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approved
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