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Search: id:A001838
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| A001838 |
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Numbers n such that phi(n+2) = phi(n) + 2.
(Formerly M2397)
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+0
9
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| 3, 5, 6, 11, 12, 14, 17, 18, 20, 29, 41, 44, 59, 62, 71, 92, 101, 107, 116, 137, 149, 164, 179, 191, 197, 212, 227, 239, 254, 269, 281, 311, 332, 347, 356, 419, 431, 452, 461, 521, 524, 569, 599, 617, 641, 659, 692, 716, 764, 809, 821, 827, 857, 881, 932, 956
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If p and p+2 are primes then p is a solution. If p and 2p+1 are both odd primes then 4p is a solution. Several numbers of the form 2^i-2 are solutions (see cross referenced sequences). Although 18 is a solution, it is not of any of these forms.
Twice Mersenne primes (cf. A000668) are also solutions. - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 14 2002
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
L. Moser, Some equations involving Euler's totient function, Amer. Math. Monthly, 56 (1949), 22-23.
D. M. Burton, Elementry Number Theory, section 7-2.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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EXAMPLE
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phi(18)+2=8=phi(18+2), so 18 is in the sequence.
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CROSSREFS
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Cf. A050472, A050473, etc. Essentially the same as A056853.
Sequence in context: A115059 A092835 A167522 this_sequence A080759 A145714 A047443
Adjacent sequences: A001835 A001836 A001837 this_sequence A001839 A001840 A001841
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Jud McCranie (j.mccranie(AT)comcast.net), Dec 24 1999
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