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A110179
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Least k such that phi(n+k)=2*phi(n), where phi is Euler's totient function.
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2
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2, 1, 2, 1, 10, 2, 6, 7, 4, 5, 14, 3, 22, 7, 2, 1, 34, 3, 18, 12, 14, 3, 46, 8, 16, 9, 10, 7, 58, 2, 30, 19, 8, 17, 30, 3, 36, 19, 26, 11, 82, 3, 86, 11, 20, 23, 94, 3, 80, 5, 34, 13, 106, 3, 68, 9, 16, 29, 118, 4, 82, 15, 10, 21, 32, 9, 94, 17, 20, 34, 142, 32, 112, 17, 48, 15, 66, 26
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Makowski shows that a k exists for each n. It appears that k<=2n. For prime n, it appears that n-1<=k<=2n.
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REFERENCES
| R. K. Guy, Unsolved Problems in Number Theory, 3rd Ed., New York, Springer-Verlag, 2004, Section B36.
Andrzej Makowski, On the equation phi(n+k)=2*phi(n), Elem. Math., 29 (1974), 13.
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MATHEMATICA
| Table[k=1; e=EulerPhi[n]; While[EulerPhi[n+k] != 2e, k++ ]; k, {n, 100}]
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CROSSREFS
| Cf. A050473 (least k such that phi(n+k)=2*phi(k)).
Sequence in context: A062347 A124781 A124151 * A071559 A071560 A097749
Adjacent sequences: A110176 A110177 A110178 * A110180 A110181 A110182
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Jul 15 2005
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