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Search: id:A001274
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| A001274 |
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Numbers n such that phi(n) = phi(n+1).
(Formerly M2999 N1215)
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+0
9
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| 1, 3, 15, 104, 164, 194, 255, 495, 584, 975, 2204, 2625, 2834, 3255, 3705, 5186, 5187, 10604, 11715, 13365, 18315, 22935, 25545, 32864, 38804, 39524, 46215, 48704, 49215, 49335, 56864, 57584, 57645, 64004, 65535, 73124, 105524, 107864, 123824, 131144, 164175, 184635
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Unlike totients, cototient[x+1] = cototient[x] never holds - except 2-Phi[2] = 3-Phi[3] = 1 - because cototient[x] congruent x modulo 2. - Labos E. (labos(AT)ana.sote.hu), Aug 08 2001
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REFERENCES
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R. Baillie, Table of phi(n) = phi(n+1), Math. Comp., 30 (1976), 189-190.
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 15, pp 5, Ellipses, Paris 2008.
R. K. Guy, Unsolved Problems Number Theory, Sect. B36.
V. L. Klee, Jr., Some remarks on Euler's totient function, Amer. Math. Monthly, 54 (1947), 332.
M. Lal and P. Gillard, On the equation phi(n) = phi(n+k), Math. Comp., 26 (1972), 579-583.
K. Miller, Solutions of phi(n) = phi(n+1) for 1 <= n <= 500000. Unpublished, 1972. [ Cf. Math. Comp., Vol. 27, p. 447, 1973 ].
L. Moser, Some equations involving Euler's totient function, Amer. Math. Monthly, 56 (1949), 22-23.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..2567 (terms less than 10^11)
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EXAMPLE
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phi(3) = phi(4) = 2, phi(15) = phi(16) = 8.
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CROSSREFS
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Cf. A000010, A001494, A051953.
Cf. A003276.
Cf. A003275
Adjacent sequences: A001271 A001272 A001273 this_sequence A001275 A001276 A001277
Sequence in context: A135903 A123184 A079486 this_sequence A139766 A003276 A136092
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KEYWORD
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nonn,easy,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 David W. Wilson (davidwwilson(AT)comcast.net)
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