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Search: id:A050473
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| A050473 |
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Smallest k such that phi(k+n)=2*phi(k). |
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+0
6
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| 2, 1, 1, 2, 1, 4, 3, 4, 3, 5, 5, 8, 26, 7, 5, 8, 9, 12, 5, 10, 7, 8, 46, 16, 5, 13, 9, 14, 7, 25, 21, 13, 9, 17, 7, 24, 62, 19, 11, 20, 76, 28, 13, 16, 15, 23, 17, 32, 21, 25, 17, 26, 52, 36, 11, 28, 13, 26, 13, 45, 74, 28, 17, 26, 13, 39, 33, 31, 21, 32, 13, 48, 39, 37, 25, 38
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Makowski proved that the sequence is well-defined.
It appears that k<=2n, with equality for the n in A110196 only. Computations for n<10^6 appear to show that k<n for all but a finite number of n. - T. D. Noe (noe(AT)sspectra.com), Jul 15 2005
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REFERENCES
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R. K. Guy, Unsolved Problems Number Theory, Sect. B36
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EXAMPLE
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phi(13+26)=24=2*phi(13), so a(13) is 26.
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MATHEMATICA
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Table[k=1; While[EulerPhi[n+k] != 2*EulerPhi[k], k++ ]; k, {n, 100}] (Noe)
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CROSSREFS
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Cf. A000010, A007015, A050472.
Cf. A110179 (least k such that phi(n+k)=2*phi(n)).
Adjacent sequences: A050470 A050471 A050472 this_sequence A050474 A050475 A050476
Sequence in context: A053000 A002070 A106052 this_sequence A057593 A117008 A126127
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KEYWORD
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nonn
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AUTHOR
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Jud McCranie (j.mccranie(AT)comcast.net), Dec 24 1999
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